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VIMS Articles Virginia Institute of Marine Science

2001

Swimming mechanics and behavior of the shallow-water brief squid Lolliguncula brevis

Ian K. Bartol

Mark R. Patterson Virginia Institute of Marine Science

Roger L. Mann Virginia Institute of Marine Science

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Recommended Citation Bartol, Ian K.; Patterson, Mark R.; and Mann, Roger L., Swimming mechanics and behavior of the shallow- water brief squid Lolliguncula brevis (2001). Journal of Experimental Biology, 204, 3655-3682. https://scholarworks.wm.edu/vimsarticles/1452

This Article is brought to you for free and open access by the Virginia Institute of Marine Science at W&M ScholarWorks. It has been accepted for inclusion in VIMS Articles by an authorized administrator of W&M ScholarWorks. For more information, please contact [email protected]. The Journal of Experimental Biology 204, 3655–3682 (2001) 3655 Printed in Great Britain © The Company of Biologists Limited 2001 JEB3819

Swimming mechanics and behavior of the shallow-water brief squid Lolliguncula brevis Ian K. Bartol1,*, Mark R. Patterson2 and Roger Mann2 1Department of Organismic Biology, Ecology, and Evolution, 621 Charles E. Young Drive South, University of California, Los Angeles, CA 90095-1606, USA and 2School of Marine Science, Virginia Institute of Marine Science, College of William and Mary, Gloucester Point, VA 23062-1346, USA *e-mail: [email protected]

Accepted 6 August 2001

Summary Although squid are among the most versatile swimmers decreased angles of attack and swam tail-first. Fin motion, and rely on a unique locomotor system, little is known which could not be characterized exclusively as drag- or about the swimming mechanics and behavior of most lift-based propulsion, was used over 50–95 % of the squid, especially those that swim at low speeds in inshore sustained speed range and provided as much as 83.8 % of waters. Shallow-water brief squid Lolliguncula brevis, the vertical and 55.1 % of the horizontal thrust. Small ranging in size from 1.8 to 8.9 cm in dorsal mantle length squid (<3.0 cm DML) used different swimming strategies (DML), were placed in flumes and videotaped, and the from those of larger squid, possibly to maximize thrust data were analyzed using motion-analysis equipment. benefits from vortex ring formation. Furthermore, brief Flow visualization and force measurement experiments squid employed various unsteady behaviors, such as were also performed in water tunnels. Mean critical manipulating funnel diameter during jetting, altering arm −1 swimming speeds (Ucrit) ranged from 15.3 to 22.8 cm s , position and swimming in different orientations, to boost and mean transition speeds (Ut; the speed above which swimming performance. These results demonstrate that squid swim exclusively in a tail-first orientation) varied locomotion in slow-swimming squid is complex, involving from 9.0 to 15.3 cm s−1. At low speeds, negatively buoyant intricate spatial and temporal interactions between the brief squid generated lift and/or improved stability by mantle, fins, arms and funnel. positioning the mantle and arms at high angles of attack, directing high-speed jets downwards (angles >50 °) and Key words: squid, negative buoyancy, hydrodynamics, swimming, using fin activity. To reduce drag at high speeds, the squid jet propulsion, Lolliguncula brevis, fin.

Introduction Resistive and propulsive forces associated with jet DeMont (Anderson and DeMont, 2000) focus on the propulsion have been investigated in scallops (Trueman, 1975; hydrodynamics and mechanics of squid locomotion. Johnson Vogel, 1985; Dadswell and Weihs, 1990; Millward and Whyte, et al. (Johnson et al., 1972) outline a theoretical approach to 1992; Cheng and DeMont, 1996; Cheng et al., 1996), jellyfish squid swimming, but it has limited applicability since it is (Daniel, 1983; Daniel, 1985; DeMont and Gosline, 1988), based on one contraction of the mantle musculature and salps (Madin, 1990) and frogfishes (Fish, 1987). The best- incorporates a number of oversimplifications and assumptions. known jetters are cephalopods, including the chambered O’Dor (O’Dor, 1988) provides a more in-depth and Nautilus, octopuses, cuttlefishes and squid. Much of the informative examination of the forces acting on adult squid hydrodynamic work on cephalopods has been performed on Loligo opalescens (and to a lesser extent Illex illecebrosus) Nautilus and centers around the effects of the shell on using video analysis and recordings of mantle cavity pressure. surrounding flow, locomotion and mode of life (Raup, 1967; Anderson and DeMont (Anderson and DeMont, 2000) provide Chamberlain and Westerman, 1976; Chamberlain, 1976; interesting information on propulsive efficiency and some Chamberlain, 1980; Chamberlain, 1981; Chamberlain, 1990; unsteady hydrodynamics of adult Loligo pealei. Holland, 1987; O’Dor et al., 1990). Although there are a The limited research on squid swimming mechanics is number of papers examining swimming energetics of squid surprising given the versatility of squid as swimmers. Squid (O’Dor, 1982; Webber and O’Dor, 1985; Webber and O’Dor, may hover in one spot, change direction rapidly with apparent 1986; O’Dor and Webber, 1986; O’Dor and Webber, 1991; ease, stop and reverse direction and ascend and descend almost O’Dor et al., 1994; Finke et al., 1996), only Johnson et al. vertically. Squid are capable of such impressive maneuvers (Johnson et al., 1972), O’Dor (O’Dor, 1988) and Anderson and because of interactions between three systems: (i) the jet, 3656 I. K. Bartol, M. R. Patterson and R. Mann which may be directed using a funnel maneuverable within a (50–100 cm s−1) (O’Dor, 1982; O’Dor, 1988; Webber and hemisphere below the body, (ii) the fins, which may undulate O’Dor, 1986) and use their fins primarily for maneuvering and and/or flap independently or synchronously, and (iii) the arms, steering (O’Dor, 1988; Hoar et al., 1994), L. brevis appears to which may be positioned at different angles of attack, moved swim at lower speeds (<30 cm s−1), uses considerable fin vertically and laterally and extended and retracted to maximize activity and swims readily in either an arms-first or a tail-first and minimize surface area. orientation (Bartol et al., 2001b). Moreover, there is metabolic Although O’Dor (O’Dor, 1988) and Anderson and DeMont evidence suggesting that brief squid have high swimming costs (Anderson and DeMont, 2000) provide important information at low speeds because of negative buoyancy and have parabolic on moderately large squid species, which swim at moderate to oxygen consumption/speed relationships (Bartol et al., 2001b), high speeds and rely heavily on the jet for propulsion, several which to date have not been detected in Illex illecebrosus, important areas of locomotion in squid remain unexplored. (i) Loligo opalescens and Loligo pealei. Little is known about how swimming mechanics change with To provide insight into how size, swimming orientation, size in squid. With the exception of some general observations unsteady phenomena, fin activity, arm motion and other on Illex illecebrosus hatchlings in aquaria (O’Dor et al., 1985), behaviors affect the swimming mechanics of slow-swimming all hydrodynamic work on squid has focused on adults of squid, brief squid Lolliguncula brevis of various sizes similar size. (ii) Squid are capable of swimming in two swimming in flumes were videotaped, and the footage was orientations: tail-first, in which the posterior closed end of the analyzed using motion-analysis equipment. Subsequent mantle and fins are located at the leading edge and the arms hydrodynamic calculations were based on these data. Flow trail behind, and arms-first, in which the arms are at the leading visualization and force measurement experiments using live edge and the fins and mantle trail behind. However, very little squid and/or models were also performed to investigate is known about arm-first swimming, which is frequently particular aspects of swimming, such as the characteristics of observed in the field and in captivity (Hanlon et al., 1983; the jet wake and the magnitude of lift and drag forces. Because Vecchione and Roper, 1991) and is the primary swimming brief squid appear to possess a unique parabolic relationship mode used for prey capture (Hanlon and Messenger, 1996; between oxygen consumption rate and speed and appear to Kier and van Leeuwen, 1997). (iii) Although the effects of swim over a more restricted speed range than other squid unsteady flow play integral roles in force and lift generation in examined to date, particular emphasis was placed on the effects other aquatic organisms (Daniel, 1983; Daniel, 1984; Daniel, of speed on swimming mechanics. 1988; Dickinson, 1996; Westneat, 1996; Müller et al., 1997; Drucker and Lauder, 1999; Dickinson et al., 2000), unsteady flow effects on squid, which swim in a pulsatile fashion, have Materials and methods received little attention, with the notable exception of a recent Experimental animals study by Anderson and DeMont (Anderson and DeMont, From May to November 1996–1998, brief squid 2000). (iv) Little is known about the swimming mechanics of Lolliguncula brevis (Blainville) were captured by trawl within slow-moving squid, which maneuver in complex, inshore embayments along the seaside of Virginia’s Eastern Shore and environments and appear to use considerable fin motion. (v) within the Chesapeake Bay near Kiptopeke, Virginia. Squid Finally, the role of the arms in locomotion and the interactions captured along the Eastern Shore of Virginia were transported between the funnel, fins and arms while swimming are not fully to the Virginia Institute of Marine Science (VIMS) Eastern understood. Shore Laboratory in Wachapreague, Virginia, while squid The brief squid Lolliguncula brevis differs in ecology and captured in the Chesapeake Bay were transported to the VIMS physiology from the squid Loligo opalescens, Loligo pealei main campus in Gloucester Point, Virginia. Squid were kept and Illex illecebrosus considered in past hydrodynamic studies alive in the field using 114 l coolers equipped with filtration and is an excellent candidate with which to investigate the and aeration systems, which were powered by sealed issues described above. The brief squid is the only cephalopod rechargeable batteries. At Wachapreague and Gloucester Point, known typically to inhabit low-salinity estuaries (Vecchione, squid were kept in flow-through raceway tanks for at least 1 1991; Bartol et al., 2001a). Using physiological mechanisms week prior to experimentation and fed ad libitum on a diet of we do not yet fully understand, it is capable of tolerating grass shrimp Palaemonetes pugio. In total, 32 squid ranging salinities as low as 17.5 ‰ under laboratory conditions from 1.8 to 8.9 cm in dorsal mantle length (DML) were (Hendrix et al., 1981; Mangum, 1991). Brief squid have short examined for this study. rounded bodies, large rounded fins, third arms with heavy keels and often reside in shallow, complex, temporally variable Flow tunnels environments (Hixon, 1980; Bartol et al., 2001a). Conversely, Three flumes were used for live animal work; flume Loligo opalescens, Loligo pealei and Illex illecebrosus are selection depended on capture location and squid size. Squid larger, more elongate and reside in deeper, more pelagic less than 3.0 cm in DML were examined in a portable 16 l regions (Hixon, 1980; Hixon, 1983; O’Dor, 1983; Hanlon recirculating flume (Vogel and LaBarbera, 1978) with a and Messenger, 1996). While Illex illecebrosus and Loligo 10 cm×10 cm×75 cm working section. Flow velocity was opalescens frequently swim at moderate to high speeds controlled in the tunnel with two propellers in a rotor-stator Swimming mechanics and behaviour of Lolliguncula brevis 3657 configuration powered by a 187 W (0.25 horse power) variable- transferred to 10 % buffered formalin. Preserved specimens speed motor. Experiments on larger squid captured at were used later for wetted surface area and aspect ratio Wachapreague and Gloucester Point, Virginia, were conducted calculations. For many of the squid considered in this study, in a 5 m long, gravity-fed recirculating flume with a the volumes of the mantle tissue (with the fins removed) and 35 cm×50 cm×100 cm working section [for a description, see internal viscera were measured after over-anesthesia by Orth et al. (Orth et al., 1994)] and a 3 m long Vogel/LaBarbera- determining the volume of water displaced by the tissues in type flume with a 15 cm×20 cm×100 cm working section [see graduated cylinders (±0.1 ml). However, for some of the squid, Patterson (Patterson, 1984)], respectively. To calibrate velocity this step was performed after preservation. For these squid, settings and to determine boundary layer thickness in each of corrections based on volume measurements performed both the three flumes, flow velocities were measured from the flume before and after preservation (on other squid) were necessary floor to the water surface (in 1.0 cm increments) over a range to account for minor shrinkage. of motor/valve settings using an acoustic Doppler velocimeter Video footage of three squid within each of four size classes (ADV) (Son-Tek, Inc., San Diego, CA, USA). (1.0–2.9 cm DML, 3.0–4.9 cm DML, 5.0–6.9 cm DML and 7.0–8.9 cm DML) was analyzed using a Sony EVO-9700 Critical and transition swimming speeds editing deck and a Peak Motus V.3.0 video and computer Lolliguncula brevis (N=32) were allowed to acclimate to the motion measurement system (Peak Performance Technologies flumes at flow velocities of 6–9 cm s−1 until they were capable Inc., Englewood, CO, USA). For the Hi-8 footage, the data of swimming steadily against the flow, which generally were analyzed at 30 frames s−1. For the high-speed footage, occurred within 15 min. After the acclimation period, squid where as many as 1000 frames s−1 were recorded, the data were were exposed to a flow velocity of 3 cm s−1 for 15–30 min. analyzed at 32 frames s−1. Not all the frames in the high-speed Speed was subsequently increased by 3 cm s−1 every 15 min footage were analyzed because the features of interest could be until the squid could no longer keep pace with free-stream followed easily at 30–32 frames s−1. For all 12 squid, 2.0–2.5 s flow. Critical swimming speed (Ucrit) was calculated using the of footage (3–6 jet cycles) was examined at each swimming equation (Brett, 1964): speed (range: 3–36 cm s−1). At speeds at which squid swam in both tail-first and arms-first orientations, footage of swimming U = U + [(T /T )U ], (1) crit l f i i in both modes was analyzed. The criteria for selecting video where Ul is the last speed at which the squid swam for the footage were as follows: (i) the squid had to be at least 5 cm entire 15 min period, Tf is the time the squid swam at the final above the flume floor and away from the flume sides (5 cm was test speed, Ti is the time spent swimming at each speed the vertical distance above which boundary-layer effects −1 (15 min) and Ui is the velocity increment (3 cm s ). within the tunnels were minimal on the basis of ADV During the critical swimming trials, many squid swam measurements and at which speeds most closely matched in two different orientations: tail-first and arms-first. The calibration settings); (ii) the squid had to swim perpendicular transition speed (Ut) at and above which these squid swam to the major axis of the camera, which was determined from exclusively in the tail-first orientation was recorded. aerial views provided by the mirror; and (iii) the squid had to begin and end at the same horizontal position after a period of Swimming kinematics 2.0–2.5 s to ensure that it was swimming at a net velocity that During the 15 min swimming periods, squid were frequently matched the free-stream flow. videotaped using either a Sony Hi-8 or Kodak Ektapro high- The following variables were measured on a frame-by-frame speed video camera. The long axis of the camera was basis using the Peak Motus motion system: mantle, arm and positioned perpendicular to the side of the flume, which funnel angles of attack relative to free-stream flow; funnel provided a lateral view of the swimming squid. A mirror was diameter (measured laterally at the location where water exits also placed within the field of view of the camera above the the funnel); mantle diameter (measured at a point 60 % of the flume at 45 ° to provide aerial views or simultaneous mantle length from the tail); fin-beat frequency (beats s−1); fin aerial/lateral views of the swimming squid when necessary. amplitude (measured at the location where chord length was Reference scales were placed on the walls and floor of the greatest); speed of the trailing edge of the fin; distance above flumes for measurement calibration, but various landmarks on the flume bottom; swimming velocity relative to free-stream the squid, such as eye diameter, were often more useful flow (calculated from eye coordinates); and acceleration. calibration aids since the focal distance between the squid and Furthermore, the time required for expansion and contraction camera lens varied among trials. Squid were illuminated in the of the mantle and the duration of the upward and downward flumes using both fiber-optic and 1000 W halogen lights. After strokes of the fins were calculated. All the above variables were each experiment, the squid were over-anesthetized in an measured from lateral close-up views, although one variable, isotonic solution of magnesium chloride (7.5 % MgCl2.6H2O) mantle diameter, was also measured in footage with and sea water (Messenger et al., 1985), and wet mass out-of- simultaneous lateral and aerial views to determine whether water (±0.1 g), mass in-water (determined using a submerged mantle expansion and contraction were uniform laterally and spring scale) (±0.1 g), dorsal mantle length (±0.1 cm) and eye dorsally. To smooth out video jitter and human error during diameter (±0.1 cm) were recorded. The organisms were then digitization, all raw coordinates were transformed using a 3658 I. K. Bartol, M. R. Patterson and R. Mann fourth-order (zero-lag) Butterworth filter (Hamming, 1983). subsequently expelled from the squid during jetting. Footage of Optimal cut-off frequencies were determined using the the dye released from the funnel was recorded using Hi-8 video. Jackson–Knee method and did not exceed 40 % of the Since squid swim at various angles of attack relative to free- sampling frequency (Jackson, 1979) (Peak Motus User’s stream flow, it was of interest to determine the angles at which Guide, 1997). Although Walker (Walker, 1998) recommends flow separation occurs. Therefore, a plaster-of-Paris cast of the a quintic spline rather than a Butterworth algorithm for body (mantle, fins and head) and third (III) pair of arms was biological data, the Butterworth filter consistently fitted the raw constructed from a 6.5 cm DML L. brevis. A conical, less- data better than either the cubic spline filter or the Fast Fourier detailed cast of the remaining arm assemblage was also made. Transform filter provided in the Peak Motus software. Aquasil impression material (Dentsply International Inc., However, given that Walker (Walker, 1998) found that Milford, DE, USA) was poured into the molds and allowed to Butterworth filters may underestimate maximum accelerations dry. The final model consisted of a main body and fins attached by approximately 16 %, it at least should be mentioned that our via embedded wire to the third arm pair and the conical section, peak accelerations may be underestimates. which represented the remaining arms. The arms were connected using embedded wire to allow for independent Flow visualization manipulation from the main body. The model was made with The velocity of water expelled from the funnel during mantle the fins fully extended rather than flush against the body contraction was calculated by seeding the flume water with brine because the fins were active over most of the speed range. shrimp eggs (Argent Chemical Laboratories), videotaping the The model was attached ventrally to a support stand and trajectory of particles ejected from the funnel using a Kodak placed in a recirculating water tunnel, which had a high-speed video camera (500–1000 frames s−1), and calculating 31 cm×40 cm×240 cm working section, located at the NASA particle velocities using the Peak Motus motion system. In total, Langley Research Center (LaRC), Hampton, Virginia. The 10 squid ranging from 3.0 to 7.8 cm DML were examined model was oriented both tail-first and arms-first, and the mantle between speeds of 3.0 and 30.0 cm s−1 swimming in tail-first and and arms were positioned independently at various angles of arms-first orientations. Three types of jet propulsion efficiencies attack (0–50 °) relative to free-stream flow. At the anteriormost were calculated: (i) Froude propulsion efficiency (ηF), (ii) rocket stagnation point, dye was injected into the water using a NASA motor propulsion efficiency (ηr) and (iii) whole-cycle dye-injection system, and flow patterns were videotaped using propulsion efficiency (ηwc) (Vogel, 1994; Anderson and Hi-8 video. DeMont, 2000). The equations used are listed below. Force measurements η F = 2U/(Uj + U) , (2) The model was attached to a force beam containing strain gauges positioned to measure forces parallel (drag) and (2UUj) η = , (3) perpendicular (lift) to free-stream flow. Signals from the strain r 2 2 (U + Uj ) gauges were amplified using an Omega DMD-465WB strain gauge amplifier, and flow velocity, which was measured (2UUj) simultaneously with force measurements, was recorded using η = , (4) wc 2 2 (2UrU + 3U + Uj ) the serial output of the Son-Tek ADV. The models were oriented tail-first and arms-first in the direction of free-stream where U is the free-stream swimming velocity, Uj is the flow, and the arms and mantle were positioned at various horizontal component of the velocity of water expelled from combinations of angle of attack that were representative of the funnel and Ur is the velocity of water entering the mantle behavior videotaped previously. Generally, angles of attack during refilling. Uj was determined from tracking particles varied from 0 to 50 °, and the angle of attack of the leading ejected from the funnel, while Ur was assumed to be equal to body section, whether it was the mantle or arms, rarely the swimming velocity of the squid. exceeded the angle of attack of the trailing body section. To Flow visualization studies of broad-scale characteristics of reduce the number of arm/mantle combinations, the arms and the jet wake were also performed. Two squid (mean mantle were positioned in 10 ° increments. Drag and lift DML=4.2 cm) were anesthetized in an isotonic solution of measurements were performed in the water tunnel at NASA −1 MgCl2 (7.5 % MgCl2.6H2O) and sea water (Messenger et al., LaRC at four flow velocities (6, 12, 18 and 24 cm s ) for each 1985). A 1.5 mm diameter hole was subsequently bored into the combination of orientation (arms-first or tail-first), arm angle lateral mantle wall using a hypodermic needle, and 3.0 m of (0–50 °) and mantle angle (0–50 °). Tygon tubing (1.5 mm outer diameter) was threaded through the Acceleration reaction measurements were performed using hole. A small bead of silicone placed at one end of the tubing the same model placed in the Gloucester Point flume, which prevented dislodgment from the mantle wall. After surgery, was smaller but capable of generating higher accelerations than each squid was placed in a 378.5 l aquarium filled with aerated the NASA LaRC tunnel. For these experiments, the model was sea water and allowed to recover. After recovery, dye (food again oriented tail-first or arms-first relative to free-stream coloring or fluorescene) or milk was pumped slowly into the flow, and the arms and mantle were positioned at various mantle cavity using a peristaltic pump, and plumes of dye were representative angle combinations (the arms and mantle were Swimming mechanics and behaviour of Lolliguncula brevis 3659 positioned in 10 ° increments). Forces parallel to free-stream mantle/arm angle combination into the steady-state drag 2 flow and velocity measurements were recorded using the force- equation (drag=GCDρwSwU ), where U is flow velocity 2 s after beam arrangement described above and the Son-Tek ADV, acceleration from rest. Mean added mass coefficients were respectively, as flow speed was elevated rapidly from 0 calculated for each mantle/arm angle combination at each of to approximately 45–70 cm s−1. Four separate trials were the two swimming orientations. performed for each orientation and mantle/arm angle To provide an estimate of the effects of the fins on drag and combination. lift forces, additional force experiments were conducted in a Data acquisition for all force measurements was water tunnel (working section 61 cm×45.7 cm×244 cm) at the accomplished using LabVIEW software (National California Institute of Technology, Pasadena, CA, USA. Instruments), a 16-bit analog-to-digital converter (National Experiments were performed using the model described above Instruments) and an Apple Macintosh G3 computer. Using a positioned at similar angles of attack and exposed to similar LabVIEW Virtual Instrument (VI) developed by the authors, flow velocities. For one set of experiments, the model with force and velocity measurements were recorded simultaneously attached fins was used; for a second set of experiments, the to a file at a scan rate of 250 Hz for 10 s for each combination model with fins removed was used. Force measurements were of variables (i.e. orientation, mantle angle, arm angle and collected using three Interface 2.25 kg strain gauge load cells trial/speed). For acceleration reaction measurements, (Interface, Inc. Scottsdale, AZ, USA) [two load cells measured accelerations 2 s after flow was increased from rest were forces normal to flow (lift), and one load cell measured forces computed from velocity measurements. Accelerations in the parallel to flow (drag)] connected to a customized force flow tank ranged from 22 to 34 cm s−2, which is similar to peak balance (Lisoski, 1993). Output from the load cells was accelerations reached by free-swimming squid at speeds of amplified using three Interface SGA amplifiers/conditioners 15 cm s−1 or below. At speeds above 15 cm s−1, free-swimming and was recorded using a Dash 8 series data recorder (Astro- squid reach much higher accelerations (e.g. 120 cm s−2), but Med, Inc.). Data were collected at 200 Hz for 10 s. these accelerations could not be re-created in our water tunnels. Within the LabVIEW VI, drag, lift and added mass Hydrodynamics coefficients were calculated continuously during the Using the coefficients computed from force measurements experiments using two equations. The equation used for drag described above, instantaneous drag, lift and acceleration coefficient (CD) and lift (CD) coefficient calculations was as reaction forces were calculated on a frame-by-frame basis for follows: three squid swimming at speeds ranging from 3–24 cm s−1. The three squid, which were 1.8, 4.4 and 7.6 cm in DML, were C or C = 2F/(ρ S U2), (5) D L w w selected (i) because they were representative of the size range where F is the force parallel to free-stream flow (for drag considered in this study, (ii) because they were particularly calculations) or perpendicular to free-stream flow (for lift cooperative and (iii) because they swam in both orientations −1 calculations), ρw is the density of fresh water at 22 °C (tail-first and arms-first) for many speeds at or below 12 cm s . −3 (998 kg m ), Sw is the wetted surface area of the model and U For each digitized frame, the steady components of drag (D) is the free-stream velocity. The wetted surface area of the and lift (L) were calculated using the equations: 2 2 models (±0.1 cm ) was determined by covering the model with D = GCDρwSwU , (7) aluminum foil, cutting the foil so that it lay flat on a piece of L = GC ρ S U2 . (8) paper, tracing the outline of the foil, cutting the tracing out, L w w weighing it and comparing its mass with that of paper of known Drag and lift coefficients measured from the models were used area. Mean drag and lift coefficients were calculated for each for these equations. Since coefficients derived from the models mantle/arm angle combination at each swimming orientation. were measured at 10 ° intervals, mantle and arm angles Since the model was stationary and the fluid around the recorded in the video frames were rounded to the nearest 10 ° model was accelerating during acceleration reaction trials, the and assigned appropriate coefficients. For speeds at which the following equation was used to calculate the added mass fins were employed, drag and lift coefficients measured from coefficient (Denny, 1993): models with extended fins were used, whereas for speeds at which the fins were not employed, drag and lift coefficients C = [(F − F )/(ρ V a ) − 1] , (6) A 1 2 w 1 1 measured from models without fins were used. A seawater −3 where CA is the added mass coefficient, F1 is the instantaneous density of 1023 kg m was used for ρw. For wetted surface area force acting parallel to free-stream flow recorded 2 s after flow (Sw) calculations, the head and arms of each squid were treated was accelerated from rest, F2 is the force acting parallel to free- as a right cone with height equal to the distance from the head stream flow under steady-state flow conditions at the velocity to the tip of the third (III) arm pair and radius equal to the mean recorded 2 s after flow was accelerated from rest, ρw is the of the dorsal and lateral head radii. The surface area of the cone −3 density of fresh water at 22 °C (998 kg m ), V1 is the volume was πrs, where r was the mean radius and s was the hypotenuse of the model and a1 is the acceleration of the water relative to of the mean radius and height. For wetted surface area 2 the model 2 s after flow was accelerated from rest. F2 was calculations (±0.1 cm ) of the remainder of the body, the calculated by inserting CD computed above for the appropriate mantle and fins were cut, placed flat on a sheet of paper and 3660 I. K. Bartol, M. R. Patterson and R. Mann traced. The paper was cut out, weighed and compared with the circumferential expansion of the mantle was assumed.) A mass of paper of known area. In addition to calculating drag linear regression of the volumetric sum of the cylinders and and lift values for each digitized frame, mean drag and mean cone (computed in each video frame throughout several jet lift values for each video sequence were computed. cycles) on mantle diameter (measured at a point 60 % of the Because the squid were accelerating within the flume, the mantle length from the tail in each video frame throughout the following equation was used to compute the acceleration jet cycles) was performed. This regression equation allowed reaction (RA) (Denny, 1993): the external volume to be predicted from mantle diameter. For each frame of video, subtracting the volume of the mantle R = ma + C ρ V a . (9) A 2 A w 2 2 tissue (without fins) and internal viscera from the external The term m is the instantaneous mass of the squid (kg), which volume determined the volume of water within the mantle. was the mass of the squid without water in its mantle cavity The volume of expelled water per time (Vw/t) was simply the plus the mass of water in the mantle cavity (see jet thrust difference in internal mantle water volume between frames calculations for mantle water volume determinations). The divided by the frame rate. term a2 is the instantaneous acceleration of the squid, CA is the Since the funnel was oriented at various angles relative to added mass coefficient for the appropriate mantle/arm angles free-stream flow throughout the jet cycle, jet thrust was divided and ρw is the density of sea water. The term V2 is instantaneous into horizontal and vertical components using the equations: volume, which was the volume of the fins, arms and head T = T cosβ , (11) plus the external volume of the mantle throughout the jetting j(h) j period (see jet thrust calculations for external mantle volume Tj(v) = Tjsinβ, (12) determinations). As was the case for drag and lift where β is funnel angle. Over a video sequence, the vertical force measurements, mantle and arm angles were rounded to the components should equal the buoyant weight of the squid if nearest 10 ° for simplicity, and the appropriate added mass altitude is maintained. On the basis of weight measurements coefficients were used in frame calculations. In addition to the made in air and water, the water/air weight ratio was instantaneous acceleration reaction computed for each 0.034±0.012 (mean ± S.D., N=12) for L. brevis, which is digitized frame, an overall mean acceleration reaction for each remarkably similar to the water/air weight ratio of 0.033 video sequence was calculated. measured for Loligo opalescens (O’Dor, 1988). Given this ratio, During the contraction phase of the jet cycle, water is buoyant weight (B) is 0.034mg, where m is the mass of the squid forcibly ejected from the mantle cavity through the funnel to (kg) and g is the acceleration of gravity (9.81 m s−2). Although generate thrust. Jet thrust (T ) may be calculated using the j squid did not begin and end video sequences at the same altitude, equation (Daniel, 1983; O’Dor, 1988): as was the case for horizontal position, vertical altitude did not Tj = Ujρw(Vw/t) , (10) differ dramatically at the beginning and end of video sequences (see Table 4). Therefore, the following equation is a reasonable where U is the velocity of water expelled from the funnel, ρ j w predictor of the balance of vertical forces at the end of the video is the density of sea water (1023 kg m−3) and V is the volume w sequence: of water expelled over time (t). U was determined using the j B = T + T + L , (13) flow visualization studies described above and was considered j(v) f(v) to be constant throughout the contraction phase of the jet where B is buoyant weight, Tj(v) is mean vertical jet thrust, Tf(v) cycle. O’Dor (O’Dor, 1988) determined that changes in jet is mean vertical fin thrust and L is mean lift over the video velocity during the jet cycle are negligible, contributing only sequence. Two values of lift were considered in the above 0.5–1.0 % of the total jet thrust over the speed range. Thus, an equation: (i) the lift of the body with extended fins and (ii) the assumption of a constant Uj should not lead to significant lift of the body without fins. This was carried out to predict the errors in thrust calculations. To determine the volume of total lift (passive and active) generated by the fins. Direct fin expelled water (Vw), mantle outlines visible in frames of thrust measurements, like wing thrust measurements, are lateral video footage were divided into a series of cylinders complex and require high-resolution flow visualization of and a cone, which represented the posterior tip of the mantle, wake structure (Rayner, 1979; Blake, 1983a; Blake, 1983b; using the Peak Motus motion system. Division of the mantle Ellington, 1984; Spedding et al., 1984; Dickinson and Götz, into a series of cylinders and a cone was accomplished by 1996; Drucker and Lauder, 1999), precise force measurements sectioning the mantle of the three squid into a series of equally of the oscillating appendage (Dickinson and Götz, 1996; spaced segments over several jet cycles. The distance between Lehmann and Dickinson, 1997) and/or three-dimensional adjacent segments was considered to be the height of a given kinematic footage (Lauder and Jayne, 1996; Westneat, 1996). cylinder or cone; heights varied from 0.20 to 0.60 cm These procedures were beyond the scope and resources of this depending on the size of the squid. The radius of each cylinder project. However, given that B, Tj(v) and L were known, the was simply half the mean of the two segments forming the mean vertical fin thrust (Tj(v)) over the video sequence could cylinder; the radius of the cone was half the segment forming be estimated using equation 13. the cone base. (Given that differences in mantle diameter The horizontal thrust forces should be equal to the horizontal viewed aerially and laterally were negligible, uniform resistive forces if there is no acceleration or deceleration. Swimming mechanics and behaviour of Lolliguncula brevis 3661

Therefore, at the end of each video sequence when there was size class, d.f.=3,75, F=6.59, P=0.0005). Subsequent a no net velocity change: posteriori Student–Newman–Keuls (SNK) tests revealed that the funnel was oriented at the greatest angle of attack, the arms T + T = F + D + R , (14) j(h) f(h) r A were positioned at a higher angle of attack than the mantle (see where Tj(h) is mean horizontal jet thrust, Tf(h) is mean Fig. 2) and squid 3.0–4.9 cm in DML had the lowest overall horizontal fin thrust, Fr is the mean refilling force, D is mean angles of attack. Moreover, in the tail-first swimming mode, drag and RA is the mean acceleration reaction over the video the angle of attack of the arms often increased briefly during sequence. The refilling force (Fr) is Fr=ρw(Vv/t)Ui, where ρw mantle expansion (refilling) (Fig. 3). is the density of sea water, Vv/t is the amount of water entering Because of limited data, significant declines in angles of the mantle over time (t) and Ui is intake water velocity (intake attack with speed during arms-first swimming were not always water velocity was assumed to be equal to the swimming detected for all size classes. However, a clear declining trend velocity of the squid). Mean horizontal fin thrust (Tf(h) over in angle of attack of most of the body sections with increasing video sequences was calculated using equation 14 and the speed was apparent in squid of 1.0–2.9 and 3.0–4.9 cm DML, above variables. while significant declines in angles of attack with increasing speed were detected for squid of 5.0–6.9 and 7.0–8.9 cm DML (Fig. 1). Angles of attack during arms-first swimming differed Results according to body section but not according to size class (two- Critical and transition swimming speeds factor ANOVA: body section, d.f.=2,33, F=124.85, P<0.0001; Mean critical swimming speeds (Ucrit) for the four size size class, d.f.=3,33, F=2.03, P=0.1294). SNK tests revealed − classes ranged from 15.3±5.3 to 22.8±5.6 cm s 1 (means ± S.D., that, during arms-first swimming, funnel angles were greatest N=6–10); however, certain squid were capable of sustaining over the entire speed range and mantle angles of attack were much higher swimming velocities (Table 1). The majority of greater than arm angles of attack (Fig. 2). squid swam in an arms-first orientation upon initial placement To assess whether there were significant differences in into swim tunnels. Many squid continued to swim in an arms- angles of attack between tail-first and arms-first swimming first orientation or alternated between arms-first and tail-first modes, a two-factor (body section and orientation) ANOVA swimming at low speeds before switching exclusively to tail- was performed on data pooled by size class. (Only those first swimming at some higher speed. Mean transition speeds speeds at which both tail-first and arms-first swimming were (Ut), i.e. speeds above which squid swam exclusively in a tail- employed were considered.) A significant interaction between first orientation, for those squid that swam in both orientations body section and orientation was detected (two-factor − ranged from 9.0 to 15.3±2.7 cm s 1 (means ± S.D., N=2–7) ANOVA: body section×orientation, d.f.=2,78; F=31.602; (Table 1). P<0.0001). Subsequent SNK tests performed to decouple the interaction revealed that there was no significant difference Kinematic measurements between mantle angles of attack during arms-first and tail-first During tail-first swimming, angles of attack of the mantle, swimming, but that the angle of attack of the funnel was greater arms and funnel decreased with increasing speed for squid in during arms-first swimming and that the angle of attack of the all four size classes (linear regressions P<0.05; Fig. 1, Fig. 2). arms was greater during tail-first swimming. Over the speed range considered in this study, angles of attack Mantle contraction rates for squid 1.0–2.9 cm in DML during tail-first swimming differed significantly according to swimming in the tail-first swimming mode increased from body section (i.e. mantle, arms and funnel) and size class (two- 2.4±0.6 contractions s−1 at 3cms−1 to 4.1±0.9 contractions s−1 − factor ANOVA: body section, d.f.=2,75, F=14.99, P<0.0001; at 18 cm s 1 (means ± S.D., N=3) (Fig. 4). However, contraction

Table 1. Mean critical swimming speeds and ranges and mean transition speeds and ranges for four size classes of Lolliguncula brevis

Size class Ucrit mean Ucrit range Ut mean Ut range −1 −1 −1 −1 (cm DML) Ncrit (cm s ) (cm s ) Nt (cm s ) (cm s ) 1.0–2.9 8 15.3±5.3 11.9–24.1 2 9.0 9.0 3.0–4.9 10 22.8±5.6 14.8–32.4 7 10.5±1.8 8.0–12.0 5.0–6.9 8 20.5±3.5 15.0–25.5 5 12.6±2.5 9.0–15.0 7.0–8.9 6 22.2±5.3 18.1–33.7 4 15.3±2.7 12.0–18.0

The critical swimming speed (Ucrit) is the maximum velocity squid can sustain for 15 min, whereas the transition speed (Ut) is the speed at and above which squid swim exclusively in a tail-first orientation. The number of squid considered in critical speed (Ncrit) and transition speed (Nt) calculations also are listed. All error terms represent ±1 S.D. DML, dorsal mantle length. 3662 I. K. Bartol, M. R. Patterson and R. Mann

Tail-first Arms-first 90 90 1.0–2.9 cm DML 80 A 1.0–2.9 cm DML 80 B 70 Fun: y = −3.23x + 67.53 70 60 r2 = 0.93, P = 0.0018 60 50 50 Arm: y = −2.01x + 40.27 40 40 r2 = 0.96, P = 0.0060 30 30 Mantle 20 Man: y = −1.14x + 20.23 20 Arms 10 r2 = 0.96, P = 0.0007 10 Funnel 0 0 0 5 10 15 20 25 0 5 10 15 20 25 90 90 80 C 3.0–4.9 cm DML 80 D 3.0–4.9 cm DML Fun: y = −1.69x + 56.01 70 70 r2 = 0.89, P = 0.0029 60 60 50 Arm: y = −1.02x + 29.27 50 40 r2 = 0.80, P = 0.0026 40 30 30 Man: y = −0.63x + 17.58 20 20 r2 = 0.92, P = 0.0002 10 10

r ee s ) (deg 0 0 0 5 10 15 20 25 0 5 10 15 20 25

atta c k 90 90

o f 80 E 5.0–6.9 cm DML 80 F 5.0–6.9 cm DML − − 70 Fun: y = 1.51x + 50.56 70 Fun: y = 2.97x + 81.56 r2 = 0.85, P = 0.0029 r2 = 0.92, P = 0.010 A n g l e 60 60 50 Arm: y = −2.30x + 53.76 50 Arm: y = −0.540x + 12.82 40 r2 = 0.93, P = 0.0004 40 r2 = 0.38, P = 0.046 30 30 − − 20 Man: y = 1.59x + 39.36 20 Man: y = 2.09x + 36.69 2 2 10 r = 0.92, P = 0.0007 10 r = 0.82, P = 0.035 0 0 0 5 10 15 20 25 0 5 10 15 20 25

90 90 80 G 7.0–8.9 cm DML 80 H 7.0–8.9 cm DML − − 70 Fun: y = 1.69x + 56.91 70 Fun: y = 1.47x + 81.14 2 2 60 r = 0.80, P = 0.0028 60 r = 0.96, P = 0.0023 50 50 − − Arm: y = 1.49x + 46.45 40 Arm: y = 0.86x + 18.34 40 r2 = 0.90, P = 0.0009 30 r2 = 0.96, P = 0.0080 30 20 20 Man: y = −0.70x + 23.33 Man: y = −0.86x + 24.21 2 10 2 10 r = 0.86, P = 0.0009 0 r = 0.70, P = 0.042 0 -10 0 5 10 15 20 25 0 5 10 15 20 25 Swimming speed (cm s-1)Swimming speed (cm s-1) Fig. 1. Mantle (Man), arm and funnel (Fun) angles of attack for Lolliguncula brevis swimming at various speeds. Results for squid swimming in a tail-first orientation are displayed in A, C, E and G, whereas those for squid swimming in an arms-first orientation are shown in B, D, F and H. Data from four size classes are included in the figure. Squid 1.0–2.9 cm in dorsal mantle length (DML) are depicted in A and B, squid 3.0–4.9 cm in DML are depicted in C and D, squid 5.0–6.9 cm in DML are depicted in E and F and squid 7.0–8.9 cm in DML are depicted in G and H. When a significant linear relationship between angle of attack and speed was detected, regression lines were plotted, and regression equations, r2 values and P values were included to the right of graphs. When significant relationships were not detected, the data points were simply connected with lines and no regression information was included. All error bars represent ± 1 S.E.M. (N=3). rates for squid belonging to larger size classes did not increase surprisingly, mean mantle contraction rate over the speed range significantly with swimming speed (range 1.6±0.2 to differed according to size class [one-factor (size class) − 2.2±0.5 contractions s 1) (means ± S.D., N=3) (Fig. 4). Not ANOVA: d.f.=3,25; F=12.726; P<0.0001]; contraction rates Swimming mechanics and behaviour of Lolliguncula brevis 3663

Tail-first

Fig. 2. Video frames of a 4.4 cm dorsal mantle length Lolliguncula brevis swimming tail-first at 3 and 24 cm s−1 (upper frames) and 3 cm s-1 24 cm s-1 arms-first at 3 and 12 cm s−1 (lower frames). Mantle and arm Arms-first angles of attack decrease with increasing swimming speed for both swimming orientations. Angle of attack differences are less pronounced for arms-first swimming because a more restricted velocity range is considered (L. brevis only swims arms-first at low to intermediate speeds). Note that the trailing body section, whether the arms during tail-first swimming or the mantle during arms-first swimming, is often positioned at higher angles of attack than the leading body section. 3 cm s-1 12 cm s-1 for squid 1.0–2.9 cm in DML were greater than those in the fins simply remained wrapped around the mantle (Fig. 4). other size classes, and no significant differences were detected Although a significant linear decline in fin-beat frequencies among squid in the larger size classes (3 cm or more in DML). with speed was not detected for squid 1.0–2.9 cm in DML, While swimming arms-first, no clear increase in mantle a clear decreasing trend in fin use with speed was apparent contraction rate with speed was apparent (Fig. 4). On the basis (Fig. 4). No significant difference in fin-beat frequency over of a one-factor (size class) ANOVA (d.f.=3,10; F=21.381; the speed range was detected between the size classes P<0.0001) performed over the speed range and subsequent a [one-factor (size class) ANOVA: d.f.=3,19; F=0.072; posteriori SNK tests, contraction rates for squid 7.0–8.9 cm in P=0.9744]. DML were lowest, and squid 5.0–6.9 cm in DML had lower Squid used fin motion for all speeds at which arms-first contraction rates than squid 3.0–4.9 cm in DML. swimming was employed, and no linear decrease in fin use When data were pooled by size class, mantle contraction with speed was detected (Fig. 4). During arms-first swimming, frequency was found to be greater during tail-first swimming squid belonging to the two smaller size classes (1.0–2.9 cm and than during arms-first swimming [one-factor ANOVA 3.0–4.9 cm DML) had greater fin-beat frequencies than squid (orientation): d.f.=1,26; F=6.536; P<0.0168]. (Again only belonging to the largest size class (7.0–8.9 cm DML) over the speeds at which both swimming orientations were used were speed range considered [one-factor ANOVA (size class): considered.) During mantle contractions, funnel diameter d.f.=3,11; F=12.36; P=0.0008]. frequently increased during the initial portion of the When data for speeds at which both swimming orientations contraction but then decreased gradually throughout the were used were pooled by size class, fin-beat frequencies were remainder of the contraction and even into mantle refilling higher during arms-first swimming than during tail-first (expansion) (Fig. 5). swimming [one-factor ANOVA (orientation): d.f.=1,26; For squid 3.0–4.9 cm, 5.0–6.9 cm and 7.0–8.9 cm in DML, F=46.39; P<0.0001] (Fig. 4). At low speeds (6 cm s−1 or swimming tail-first, fin activity decreased significantly with below) during tail-first swimming and at all speeds during swimming velocity until a velocity was reached at which the arms-first swimming, fin downstrokes often occurred during 3664 I. K. Bartol, M. R. Patterson and R. Mann mantle contraction and refilling (Fig. 3, 30 Fig. 5B), whereas at higher speeds when fin 25 activity was reduced, fin downstrokes 20 frequently occurred during mantle contractions (Fig. 5A). 15 Mantle Although contraction rates during tail-first 10 Arms Angle (degrees) swimming did not increase significantly with 5 speed for squid in the size classes 3.0–4.9 cm, 00.5 11.5 2 5.0–6.9 cm and 7.0–8.9 cm DML, mantle 1 expansion did increase with speed (linear 0.5 regressions, P<0.05; Fig. 6). However, no clear m o t io n n

increase in mantle expansion with speed was fi 0 detected for squid 1.0–2.9 cm in DML, the size -0.5

class in which mantle contraction did increase er t ic a l with swimming speed. Mantle expansion of V -1 squid swimming in an arms-first orientation did 00.5 11.5 2 not increase significantly with speed (Fig. 6). 1.65 During tail-first swimming, vertical fin motion (the absolute vertical distance between 1.6 maximum upstroke and maximum downstroke) decreased with increasing swimming velocity 1.55 (linear regressions, P<0.05), but no detectable decrease in fin amplitude was found for arms- Ma n t le d i a m e er ( c ) 1.5

) 00.5 11.5 2

first swimming (Fig. 6). - 1 3 The time required for mantle expansion

e t o 2 during tail-first swimming was greater than that v

w ( c m s 1 required to contract the mantle for squid in size 0 classes 3.0–4.9 cm, 5.0–6.9 cm and 7.0–8.9 cm -1 DML over the range of speeds considered -2 el oci t y rel at i

(paired t-test, P<0.05) (Table 2). When data V -3 from all the size classes were pooled, this f ree - s t re a m l o 00.5 11.5 2 )

difference was highly significant (P=0.0002). - 2 40 When swimming in an arms-first orientation, 30 only squid 3.0–4.9 cm in DML had greater 20 10 mantle expansion than contraction times, but 0 mantle expansion times were significantly -10 greater than contraction times when data from -20 all the size classes were pooled (P=0.0064) A cc eler at io n ( c m s -30 00.5 11.5 2 (Table 2). Mantle expansion time decreased Time (s) with increased swimming speed only for squid 1.0–2.9 cm in DML while swimming tail-first Fig. 3. Arm and mantle angles of attack, vertical fin motion (relative to the point (linear regression, P=0.0080; r2=0.857) where the fin connects to the mantle), mantle diameter, changes in linear velocity (Table 2). Mantle contraction time decreased (relative to free-stream flow) and acceleration for a 4.4 cm dorsal mantle length (DML) −1 with increasing swimming speed for squid Lolliguncula brevis swimming tail-first at 6 cm s against a current in a flume. In 1.0–2.9 cm and 3.0–4.9 cm in DML while total, 60 frames were analyzed to generate the traces. swimming tail-first (linear regression, P=0.0034, r2=0.907 for 1.0–2.9 cm DML; increase in fin speed with increasing swimming velocity was P=0.0391; r2=0.535 for 3.0–4.9 cm DML) (Table 2). detected for squid swimming tail-first (P=0.0151; r2=0.461) No significant differences between upward and downward fin (Table 2). Mean trailing edge fin speeds ranged from 4.2 to 12.3 stroke times were detected, and there was no increase or cm s−1. At swimming speeds below 9 cm s−1, trailing edge fin decrease in upward or downward fin stroke time with increasing speeds generally exceeded swimming speeds, and the trailing speed for squid swimming in either tail-first or arms-first edge fin wave resembled a sideways ‘S’. At speeds of orientations (Table 2). Furthermore, no consistent increase or 9–12 cm s−1 or above, trailing edge fin speeds were generally decrease in trailing edge fin speed with increasing swimming less than swimming speed, and the trailing fin wave more speed was detected when size classes were examined closely resembled an inverted ‘V’, with the distal portion of the separately; however, when the size classes were pooled, a linear wave at an obtuse angle relative to the oncoming water flow. Swimming mechanics and behaviour of Lolliguncula brevis 3665 ) ) 4.446 2.111 2.586 1 − =0.985; m=3.285 =0.974; m= − =0.868; m=3.223 =0.824; m=2.834 =0.555; m= − =0.575; m=0.745 =0.904; m=3.297 =0.785; m= − : P =0.9235 : P =0.0397* : P =0.0005* : P =0.0003* : P =0.7374 : P =0.2252 : P =0.4159 : P =0.0975 : P =0.5479 2 2 2 2 2 2 2 2 − r r r − − r − r r − r − − − − r ) and deceleration ( − 1 − ) speed (cm s 1 0.148 0.165 0.152 0.145 − ) speed acceleration (+) − swimming in tail-first and arms- swimming in tail-first Regression Regression =0.818; m= − =0.709; m=0.168 =0.708; m= − =0.612; m=0.193 =0.563; m= − =0.823; m=0.0183 =0.675; m= − : P =0.0439* : P =0.0039* : P =0.0088* : P =0.0133* : P =0.1156 : P =0.0659 : P =0.0869 : P =0.9200 : P =0.0897 2 2 2 2 2 2 2 − − r r − r r − r r − − − − − r ) speed (cm s 1 − Lolliguncula brevis DML . =0.461; m=0.461 2 P =0.3111 +: P =0.0824 +: P <0.0001* P =0.2833 +: P =0.0087* +: P =0.0008* P =0.6143 +: P =0.5447P =0.7694 +: P =0.2894 +: P =0.1097P =0.3601 +: P =0.7270 +: P =0.6989 +: P =0.1449 P =0.1048 +: P =0.3808 +: P =0.3660 P =0.1554 +: P =0.2391P =0.0151; +: P =0.0293* +: P =0.0004* +: P <0.0001* P =0.3155 +: P =0.0311* +: P <0.0007* r ) speed (cm s 1 − and 7.0–8.9 cm P =0.6667 P =0.6143 U: P =0.2339 U: P =0.4568 U: P =0.2116 U: P =0.8240 U: P =0.8790 D: P =0.1838 D: P =0.2557 D: P =0.1931 D: P =0.9418 U: P =0.7115 U: P =0.3347 U: P =0.4556 D: P =0.7594 D: P =0.8263 D: P =0.2134 ) speed (cm s 1 0.006 D: P =0.4065 0.004 0.0004 − Regression Regression Regression of mean maximum of Regression P =0.0080*; U: P =0.2783 P =0.8863 P =0.1888 P =0.9473 P =0.8236 P =0.3362 P =0.8580 P =0.1126 =0.857; m= − =0.907; m= − =0.535; m= − 2 2 2 C: P =0.0034* r r r C: P =0.0391*; D: C: P =0.7324 C: P =0.3437 C: P =0.8285 C: P =0.7418 C: P =0.4155 C: P =0.4726 C: P =0.3157 first orientations over a range of speeds a range orientations over first P =0.0694 E: P =0.4274 E: P =0.3325 E: P =0.2038 E: P =0.3517 E: P =0.3910 E: P =0.3933 E: P =0.8596 E: P =0.3280 E: -tests and linear regressions performed on kinematic data collected from performed on kinematic data collected from t -tests and linear regressions Paired Paired of mantle of upward Regression (+) and positive mean maximum comparison of comparison Paired and expansion and downward of trailing ( negative P =0.2856 P =0.0095*; E >C P =0.0663 P =0.0814 P =0.0064*; E>C P =0.0463*; E>C P =0.0119*; E>C P =0.0002*; E>C P =0.0245*; E>C mantle expansion mantle expansion and of upward contraction times times fin stroke edge fin speed (cm deviations s Summary of results of paired of paired Summary of results , slope; U, upward stroke time; D, downward stroke time; NA, not applicable. time; NA, stroke time; D, downward stroke time; C, contraction M , slope; U, upward tail-first; A, arms-first; E, expansion DML , dorsal mantle length; T, The four size classes considered are as follows: 1.0–2.9The four size classes considered are as follows: cm DML , 3.0–4.9 cm DML , 5.0–6.9 cm DML No statistical analyses were performed on squid in the smallest size class swimming an arms-first orientation because of limited data. Asterisks denote significance at P <0.05. Table 2. Table (cm DML ) Orientation times (s) times (s) stroke speed (cm s 1.0–2.9 T 1.0–2.93.0–4.9 A T NA5.0–6.9 NA A 7.0–8.9 NA A Pooled NA A NA NA NA Size class and contraction fin downward (s) on swimming (s) on swimming (s) on swimming on swimming on swimming 3.0–4.9 A 7.0–8.9 T Pooled T 5.0–6.9 T 3666 I. K. Bartol, M. R. Patterson and R. Mann

When tail-first swimming data from 5 5

) 1 the four size classes were pooled, - Tail-first Arms-first mean maximum positive and negative 4 4 (converted to absolute values) deviation in velocity and acceleration 3 3 were found to increase with swimming speed (P<0.0039; r2>0.675) (Table 2). Although linear relationships were not 2 2 always detected when tail-first velocity and acceleration deviations were 1 1 regressed against swimming speed and examined separately by size class, (s frequency contraction Mantle 0 0 P-values of less than 0.10 were 0 5 10 15 20 25 0 5 10 15 20 25 frequently observed (Table 2). No 1.0–2.9 cm DML: y = 0.11x + 2.03, r2 = 0.98, P = 0.0002 linear relationships between mean maximum velocity deviation and speed 5 5 and mean maximum acceleration Arms-first Tail-first

deviation and speed were detected for )

4 1 - 4 squid swimming in the arms-first orientation (P>0.05). 3 3 Flow visualization On the basis of velocity 2 2

measurements of particles expelled by

eat frequency (s frequency eat b in- squid during swimming, all three F 1 1 propulsion efficiencies were lowest at −1 −1 3cms and highest at 9 cm s , and 0 0 arms-first propulsive efficiencies 0 5 10 15 20 25 0 5 10 15 20 25 were generally higher than tail-first Swimming speed (cm s-1) efficiencies (Table 3). Rocket motor propulsive efficiencies were 3.0–4.9 cm DML: y = −0.20x + 3.62, r2 = 0.86, P = 0.006 1.0–2.9 cm DML consistently higher than Froude 5.0–6.9 cm DML: y = −0.17x + 2.96, r2 = 0.83, P = 0.007 3.0–4.9 cm DML propulsion efficiencies and, on 7.0–8.9 cm DML: y = −0.11x + 2.94, r2 = 0.88, P = 0.0006 5.0–6.9 cm DML average, whole-cycle efficiencies were lower than both Froude and rocket 7.0–8.9 cm DML motor propulsion efficiencies. When dye or milk was injected into Fig. 4. Mantle contractions frequency and fin-beat frequency for Lolliguncula brevis swimming against a steady current in a flume over a range of speeds in both tail-first and arms-first the mantle of squid (mean DML orientations. Data from four size classes are depicted: 1.0–2.9 cm, 3.0–4.9 cm, 5.0–6.9 cm and 4.2 cm), the squid appeared agitated 7.0–8.9 cm dorsal mantle length (DML). When significant linear relationships were detected, and frequently jetted abruptly and regression lines were plotted, and regression equations, r2 values and P values were included erratically across the aquarium or underneath graphs. All error bars represent ±1 S.E.M. (N=3). into the aquarium walls. During these episodes, the jet wake was generally very turbulent, and no vortex ring formation was i.e. the mantle when in the tail-first swimming mode or the observed. However, on several occasions, the squid swam arms when in the arms-first swimming mode, was at 0 ° and across the aquarium (often beginning from rest), achieving a the trailing body section was positioned at more than 30 °. speed of 8.6±2.5 cm s−1, and several vortex rings formed However, when the leading body section was at 10–20 °, in the jet wake. The mean ring radius was 4.8±1.2 cm separation did not occur until the trailing section was at 40 ° and the mean jet core radius was 2.6±0.8 cm (means ± S.D., or more. During tail-first swimming, no squid positioned N=2). its mantle at a higher angle of attack than its arms, but Obvious flow separation and the subsequent migration of during arms-first swimming, angles of attack of the arms flow along the body in a retrograde flow direction was were occasionally observed to be higher than those of the observed when the mantle and arms of models were both mantle. In flow visualization experiments using models positioned at more than 30 ° relative to flow, irrespective of oriented arms-first, separation occurred whenever the arms whether the models were positioned tail- or arms-first. were at angles of attack 10–15 ° greater than that of the Separation was also observed when the leading body section, mantle. Swimming mechanics and behaviour of Lolliguncula brevis 3667

2.6 2.55 A 2.5 2.45 2.4 2.35

Mantle diameter (cm) 00.25 0.5 0.75 11.25 1.5 1.752

0.6 0.5 0.4 0.3 0.2 0.1 0 Fu nnel diameter (cm) 00.25 0.5 0.75 11.25 1.5 1.752

2 1 0 in m o ti n (cm) f -1 -2 ertical 00.25 0.5 0.75 11.25 1.5 1.75 2 V Time (s) 2.7 2.65 B 2.6 2.55 2.5 2.45

Mantle diameter (cm) 00.25 0.5 0.75 11.25 1.5 1.75 2

0.4 0.3 0.2 0.1 0

Fu nnel diameter (cm) 00.25 0.5 0.75 11.25 1.5 1.752 Fig. 5. Mantle diameter, funnel diameter and vertical fin motion 1.5 (relative to the point where the fin 1 connects to the mantle) of a 0.5 Lolliguncula brevis (7.3 cm in dorsal 0

mantle length, DML) swimming (A) in m o ti n (cm) -0.5 − tail-first and (B) arms-first at 9 cm s 1 -1 against a steady flow in a flume. For -1.5

ertical f 00.25 0.5 0.75 11.25 1.5 1.752

each swimming orientation, 60 frames V were analyzed to generate the traces. Time (s)

Force measurements angle combinations observed in video footage of swimming Polar diagrams of drag and lift coefficients calculated from squid were included in the figures.) For the mantle/arm angle squid models with extended fins positioned in both tail-first and combinations considered, the highest lift-to-drag ratios for tail- arms-first orientations in a water tunnel are depicted in Fig. 7. first swimming were detected at mantle/arm angle The symbols displayed on the figure represent the various combinations of 0 °/30 ° (2.34) and 10 °/20 ° (2.27) (Fig. 7). mantle angles of attack, while the degree designations in colour The highest lift-to-drag ratios for arms-first swimming were on the figures represent arm angles of attack. (Only mantle/arm detected at mantle/arm angles of 20 °/0 ° (3.02) and 20 °/10 ° 3668 I. K. Bartol, M. R. Patterson and R. Mann

Table 3. Froude propulsion, rocket motor propulsion and whole-cycle propulsion efficiencies for Lolliguncula brevis swimming in both tail-first and arms-first orientations Froude propulsion efficiency (%) Rocket propulsion efficiency (%) Whole-cycle propulsion efficiency (%) Swimming speed (cm s−1)TATATA 3 28.3 57.9 32.1 69.9 29.0 44.6 6 42.4 64.0 50.1 77.1 39.5 44.6 9 57.5 74.3 69.4 87.8 44.4 43.0 12 53.8 69.9 64.8 83.0 43.9 44.0 15 48.4 57.9 42.3 18 46.0 54.9 41.3 21 40.3 47.5 38.3 24 43.8 51.9 40.2 27 45.1 52.9 41.0

A, arms-first; T, tail-first. Since the majority of squid did not swim at speeds above 12 cm s−1 in the arms-first mode, arms-first efficiencies were only calculated for speeds of 3–12 cm s−1.

0.3 0.3 Tail-first Arms-first 0.25 0.25

0.2 0.2 0.15 0.15 0.1

Mantle expansion (cm) Mantle expansion 0.1 0.05

0.05 0 0 5 10 15 20 25 0 5 10 15 20 25 3.0–4.9 cm DML: y = 0.002x + 0.10, r2 = 0.97, P < 0.0001 5.0–6.9 cm DML: y = 0.003x + 0.14, r2 = 0.97, P < 0.0001 7.0–8.9 cm DML: y = 0.004x + 0.17, r2 = 0.92, P = 0.0002

3 3 Tail-first Arms-first

2 2

in motion (cm) motion in f Fig. 6. Mantle expansion and vertical

fin motion (absolute vertical distance

tical tical r e between maximum upstroke and v 1 1 downstroke) plotted over a range of

swimming speeds for Lolliguncula

te te u sol b brevis swimming in both tail-first and A arms-first orientations. Data from four 0 0 0 5 10 15 20 25 size classes are depicted: 1.0–2.9 cm, 0 5 10 15 20 25 3.0–4.9 cm, 5.0–6.9 cm and 7.0–8.9 cm Swimming speed (cm s-1) dorsal mantle length (DML). When significant linear relationships were 1.0–2.9 cm DML 1.0−2.9 cm DML: y = −0.055x + 0.79, r2 = 0.67, P = 0.043 detected, regression lines were plotted, 3.0−4.9 cm DML: y = −0.095x + 1.78, r2 = 0.79, P = 0.018 3.0–4.9 cm DML and regression equations, r2 values and 5.0−6.9 cm DML: y = −0.096x + 2.19, r2 = 0.75, P = 0.026 5.0–6.9 cm DML P values were included underneath − − 2 graphs. All error bars represent ± 1 7.0 8.9 cm DML: y = 0.13x + 3.43, r = 0.88, P = 0.0005 7.0–8.9 cm DML S.E.M. (N=3). Swimming mechanics and behaviour of Lolliguncula brevis 3669

0.4 8.8 °/6.3 °, respectively (squid did not swim arms-first at high Tail-first speeds). Lift-to-drag ratios for low and intermediate speeds 50° (1.07) were 2.18 and 2.68, respectively. On the basis of force measurements collected from models with and without fins, the 50° 0.3 50° ° fins contributed 10–51 % of the total drag force and 0–65 % of 40° 40 (1.33) the total lift force for mantle angles of attack between 0 and 30° (1.58) 40 ° during tail-first swimming and 15–61 % of the total drag force and 4–68 % of the total lift force for mantle angles of Mantle angle 0.2 50° attack between 0 and 40 ° during arms-first swimming. 40° (1.82) 0° ° 40° 30° Added mass coefficients calculated from force 20 50° ° (2.27) 10 measurements collected from squid models are plotted in 30° 20° ° 20° Fig. 8. Added mass coefficients increased exponentially as the 0.1 10 50° 40° 30° angle of attack of the mantle and arms increased, irrespective 30° (2.34) of whether the models were positioned in the tail-first or arms- 20° 40° L ° first orientation. C 10 ° 0° 50 0 Hydrodynamics

c i en t , 00.05 0.1 0.15 0.2 0.25 0.3 0.35 Resistive and propulsive forces acting on three squid 0.4 (1.8 cm, 4.4 cm and 7.6 cm in DML) swimming tail-first and Arms-first arms-first over a range of speeds are displayed in Table 4. For L ift coe ffi all three squid, buoyant weight was greater than lift and vertical 20°30° ° ° 40° −1 20° 30 40 50° jet thrust for swimming velocities at and below 12–15 cm s 0.3 ° (see negative values in vertical force balance column of 20°30 10° (1.85) ° ° Table 4 and balance of forces in Fig. 9). Fin thrust was not 0° 0 10 (1.17) 0° 10° (1.40) calculated directly, but the force imbalance between buoyant ° weight, lift and vertical jet thrust may serve as a good 0.2 20 10° (2.98) approximation of vertical fin thrust, especially since there was 0° (3.02) little net change in altitude from the beginning to the end of the video sequences (vertical change <0.9 cm; Table 4). On the basis of the vertical force imbalance, the potential contribution 0.1 10° (2.68) 0° of the fins to upward-directed forces was substantial at low speeds (3–6 cm s−1), ranging from 28.4 to 78.6 % when models 0° (1.04) with fins were considered in force balance equations and from 42.9 to 83.8 % when models without fins were considered. The 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 contribution of the fins to upward-directed forces decreased with increasing speed. Fin activity ceased at 12, 15 and Drag coefficient, CD 18 cm s−1 for 1.8, 4.4 and 7.6 cm DML squid, respectively, and Fig. 7. Polar diagrams of drag (CD) and lift (CL) coefficients fin use predictions were in reasonable agreement with these calculated from squid models (with fins) oriented tail-first and arms- speeds. For example, only 4.1 % of the upward-directed force first relative to the free-stream flow. The various symbols, which are by the 1.8 cm DML squid was unaccounted for and assumed to described in the figure, represent the angles of attack of the mantle. be generated by the fins at 12 cm s−1, when no fin activity was Degree markings within the figures represent angles of attack of the arms. Only mantle/arm angle combinations observed during employed. swimming trials of brief squid are represented. At each mantle angle, The acceleration reaction was clearly the dominant the arm angle providing the highest lift-to-drag ratio is denoted in instantaneous horizontal force (Fig. 9, Fig. 10). Although the bold type and the ratio is provided in parentheses next to the angle. mean acceleration reaction over a video sequence was low relative to the range of instantaneous acceleration reaction values within a series of jet cycles, mean values were (2.98). On the basis of video footage of tail-first swimming, nonetheless high and variable relative to the other forces (Table mean mantle/arm angle combinations over all size classes for 4). The high variability is attributed to its sensitivity to velocity low (3 cm s−1), intermediate (12 cm s−1) and high (21 cm s−1) changes. Since the acceleration reaction should theoretically speeds were 20.9 °/33.4 °, 10.1 °/17.8 ° and 8.7 °/10.7 °, balance out over several jet cycles (Daniel, 1983), the respectively. Lift-to-drag ratios were therefore 1.78 for low horizontal force balance was calculated assuming that the mean speeds, 2.27 for intermediate speeds and 2.26 for high speeds. acceleration reaction was zero for the video sequence. (If actual On the basis of video footage of arms-first swimming, acceleration reaction forces were included in force balance mean mantle/arm angle combinations for low (3 cm s−1) equations, they would dominate the force balance and obscure and intermediate (12 cm s−1) speeds were 24.2 °/18.8 ° and fin thrust calculations.) On the basis of the horizontal force 3670 I. K. Bartol, M. R. Patterson and R. Mann balance equation, the fins appeared to 16 Arm angle contribute significantly to horizontal 15 Tail-first thrust, especially at low speeds 14 0° − (3–6 cm s 1) when the potential 13 10° 12 contribution of the fins to horizontal 20° thrust ranged from 32.0 to 55.1 % 11 30° (Table 4). As was the case for vertical fin 10 ° thrust predictions, horizontal fin thrust 9 40 predictions based on force balance 8 50° equations were in reasonable agreement 7 6 with kinematic observations; predicted ° 2 − 5 40 : y = 0.006x 0.037x + 1.00 horizontal fin thrust was less than 5 % of 2 4 r = 0.98, P = 0.006 the overall horizontal thrust when the fins 3 50°: y = 0.005x2 − 0.047x + 1.03 were inactive (Table 4). A significant A C 2 r2 = 0.97, P = 0.018 proportion of the drag in the horizontal 1 direction was a product of positioning the c i en t , 0 mantle and arms at angles of attack ffi 0 10 20 30 40 50 60 greater than 0 °, especially at low speeds (3–6 cm s−1) when as much as 91.3 % of 16 the drag was associated with the angle of 15 Arms-first Arm angle attack (Table 4). 14 0°

Added m as coe 13 10° 12 ° Discussion 11 20 ° Lolliguncula brevis 10 30 9 40° The data from this study indicate that 8 50° Lolliguncula brevis is a slow-swimming 7 squid that relies heavily on its fins for 6 locomotion, is capable of swimming in 5 0°: y = 0.003x2 − 0.047x − 0.029 two different orientations and uses various 4 r2 = 0.95, P = 0.010 swimming strategies depending on size. 3 ° 2 − Unlike other squid, such as Loligo 2 10 : y = 0.004x 0.001x + 1.08 2 opalescens and Illex illecebrosus, which 1 r = 0.98, P = 0.018 swim for sustained periods at speeds as 0 high as 50 and 100 cm s−1, respectively 0 10 20 30 40 50 60 (Webber and O’Dor, 1986; O’Dor, 1988; Mantle angle (degrees) O’Dor and Webber, 1991), L. brevis −1 Fig. 8. Added mass coefficients (CA) for Lolliguncula brevis swimming in tail-first and generally swims at speeds below 22 cm s arms-first orientations at various angles of attack. Mantle angles (degrees) are plotted on the and swims either tail-first or arms-first at x-axes and arm angles are denoted using symbols. Only mantle/arm angle combinations −1 speeds below 9–15 cm s . Because of its observed during swimming trials of L. brevis are represented. Polynomial regressions were relatively low speed range, L. brevis may performed when more than four data points were available, and these results are displayed use its fins, muscular hydrostats that next to the graphs. presumably operate effectively only at low/moderate speeds because of muscle and support structure maintain position in the water column, an energetic expense constraints (Kier, 1988; Kier, 1989; O’Dor and Webber, 1991), that is not trivial at low speeds [see Bartol et al. (Bartol et al., over a larger proportion of its speed range (0–18 cm s−1) than 2001b)]. An important mechanism used by brief squid for lift Loligo opalescens or Illex illecebrosus. Consequently, the fins generation at low speeds is the elevation of mantle and arm play a more integral role in locomotion. Moreover, not all size angles of attack, which induce downward flow, enhance the classes of squid appear to use the same swimming approaches, pressure differential above and below the body and increase with smaller squid increasing contraction rates but keeping lift (Vogel, 1994; Dickinson, 1996). Although the mantle and expelled water volume fairly constant with increasing speed, arms of squid do not resemble traditional human-made airfoils, while larger squid do the opposite. lift may be generated when the mantle (with attached fins) and arms are positioned at high attack angles (see polar diagrams). Lift and stability requirements at low speeds Lift enhancement by increasing body angles of attack has also As is the case with many squid species, L. brevis is been observed in negatively buoyant fish (He and Wardle, negatively buoyant and consequently must generate lift to 1986; Webb, 1993), ski jumpers (Ward-Smith and Clements, Swimming mechanics and behaviour of Lolliguncula brevis 3671

0.002 Vertical forces 6 5.8 0.001 5.6 5.4

Height (cm) 5.2 0 00.5 11.5 2 Time (s)

Buoyant weight -0.001 Lift Vertical jet thrust -0.002 Balance of forces

-0.003 00.25 0.5 0.75 11.25 1.5 1.75 2

Force (N) Force Horizontal forces 0.005

0.003 Drag 0.001 Acceleration reaction Horizontal jet thrust -0.001 Refilling force Balance of forces -0.003

-0.005

-0.007 00.25 0.5 0.75 11.25 1.5 1.75 2 Time (s) Fig. 9. Vertical and horizontal forces acting on a 4.4 cm Lolliguncula brevis swimming tail-first at 6 cm s−1. In the vertical forces graph, negative values represent forces acting towards the flume floor (i.e. buoyant weight), whereas in the horizontal forces graph negative values represent forces acting in the direction of free-stream flow (e.g. drag). Since there was some net altitude change over the 2 s video sequence, the height of L. brevis above the flume floor is displayed next to the vertical forces graph. There was no net horizontal change over the video sequence. Fin thrust contributions are not included in the figure.

1982), honeybees (Nachtigall and Hanauer-Thieser, 1992), surfaces on aircraft wings, such as ailerons or Fowler flaps, birds (Tobalske and Dial, 1996) and rays (Heine, 1992). which are located on the trailing edge of the wing and The trailing body section (i.e. the arms or mantle depending positioned at higher angles of attack than the main wing (and on swimming orientation) was frequently positioned at higher often extended) to increase lift (Bertin and Smith, 1989; angles of attack than the leading body section. Flow Kundu, 1990; Munson and Cronin, 1998). Just as pilots make visualization and lift measurement studies using squid models fine lift adjustments with ailerons, squid in the tail-first indicate that positioning the trailing body section at higher swimming mode frequently adjusted the angles of attack of angles of attack than the leading body section delays flow their arms (trailing body section) throughout the jet cycle and separation (when coupled with appropriate leading body extended their arms to increase surface area, especially during section angles) and elevates lift production during both tail- refilling to generate extra lift when the jet was no longer first and arms-first swimming. This is analogous to control producing any downward-directed thrust. At low speeds, the 3672 I. K. Bartol, M. R. Patterson and R. Mann 65.5 62.3 72.8 65.1 60.4 24.3 13.0 12.1 77.0 77.9 53.4 46.4 52.2 47.4 46.6 36.5 31.8 25.8 35.1 26.5 5 6 7 5 4 4 4 5 4 4 6 6 6 5 4 4 4 4 5 5 − − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 4.12 × 1.78 × 1.23 × 1.84 × 2.95 × 9.67 × 1.35 × 1.32 × 3.05 × 2.45 × − − − − − − − − − − 38.2 46.735.3 4.27 × 34.5 6.59 × 28.4 35.348.6 2.73 × 32.036.8 2.74 × 25.630.1 3.84 × 14.9 2.93 × 24.7 ) 0 5.56 × )0 ))0 0 6.02 × )) (1.6) (0.7) 9.35 × ) (2.6) 4.50 × 5 5 4 4 6 6 5 5 5 6 6 5 4 4 4 4 4 4 4 5 − − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 without contribution reaction % of drag 2.10 × 1.20 × 3.70 × 6.84 × 8.83 × 2.84 × 2.71 × 3.16 × 5.60 × 1.15 × 1.11 × 1.20 × 1.80 × 2.15 × 1.74 × 2.58 × Horizontal − − − − − − − − − − − − − ( − ( − ( − (+2.65 × (+9.30 × (+3.96 × (+2.07 × force balance Potential % Acceleration 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 − − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1.10 × 1.00 × 5.21 × 5.14 × 7.95 × 1.31 × 1.66 × 2.81 × 1.03 × 1.27 × 2.34 × 2.06 × 5.15 × 5.00 × 9.56 × 7.81 × 1.36 × 2.42 × 3.13 × 3.31 × 6 6 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 − − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Refilling Horizontal acceleration of fins to video over associated 4.00 × 5.22 × 7.35 × 2.87 × 3.27 × 4.44 × 4.63 × 5.04 × 6.73 × 1.57 × 1.32 × 1.58 × 2.67 × 8.78 × 8.48 × 8.35 × 1.31 × 1.54 × 2.27 × 2.12 × − − − − − − − − − − − − − − − − − − − − ) ) ) ) ) ) ) 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 3 3 3 3 − − − − − − − − − − − − − − − − − − − − (1.8 cm, 4.4 cm and 7.6 mantle length) swimming in both tail-first cm in dorsal 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9.30 × 1.11 × 1.28 × 1.21 × 6.48 × 6.53 × 9.53 × 1.32 × 1.49 × 2.60 × 2.45 × 5.71 × 5.61 × 9.09 × 8.27 × 1.15 × 1.81 × 2.00 × 2.29 × 2.64 × − − − − − − − − − − − − − − − − − − 0 3.7 70.1 68.5 28.4 32.2 22.9 78.6 75.0 65.7 63.6 39.3 34.3 Potential % contribution contribution )0( )0( )0( )0( )0( ) (73.7) ) (72.6) ) (42.9) ) (48.8) ) (28.2) ) (4.1) ( − ) (79.1) ) (65.6) ) (43.7) ) (39.0) ) (11.4) )) (2.8) (1.6) ( − ) (83.8) ) (67.7) 5 5 4 4 4 3 4 4 4 4 5 5 5 4 5 5 6 3 3 3 3 3 3 3 3 4 3 4 4 5 5 3 3 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Vertical Vertical of fins to 1.62 × 1.60 × 9.44 × 1.07 × 6.21 × 2.21 × 1.84 × 1.22 × 1.09 × 3.20 × 7.78 × 9.03 × 4.60 × 1.54 × 1.52 × 6.25 × 7.08 × 4.86 × 2.21 × 2.12 × 1.84 × 1.78 × 1.12 × 9.62 × 1.04 × − − − − − − − − − − − − − − − − − − − − − − − +1.94 × (2.34 × (1.90 × ( − ( − (+1.49 × (+8.51 × (+1.51 × (+8.21 × (+1.28 × and arms-first orientations over a range of speeds in a flume a range orientations over and arms-first 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 3 − − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Vertical Vertical force upward- 3.93 × 4.11 × 3.39 × 3.51 × 3.73 × 3.31 × 3.66 × 3.95 × 4.42 × 4.60 × 5.29 × 5.00 × 5.15 × )( )( )( )( )( ) 5.31 × ) 7.39 × ) 9.44 × ) )( ) )( )( )( )( )( ) 4.34 × ) 6.97 × ) 6.91 × ) 1.10 × 5 5 5 5 4 5 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 (1.86 × (1.90 × (9.17 × (7.76 × (1.21 × (1.23 × (2.19 × (5.08 × (5.20 × (1.12 × (1.18 × (1.98 × (2.21 × 0.312 5.64 × 0.9150.274 (1.61 × (2.11 × 0.188 (2.25 × 0.0841 1.34 × 0.0337 1.24 × 0.0900 2.20 × − − − − − − − ) of 1 − Mean resistive and propulsive forces computed for three Lolliguncula brevis computed for three forces and propulsive Mean resistive Swimming Table 4. Table size (cm s Squid velocity Change 1.81.8 3 A1.8 +0.104 6 T 2.81 × 1.8 +0.0920 6 A 1.24 × +0.0311 9 T 1.14 × 4.4 6 T 4.44.4 9 T 4.4 9 A4.4 +0.0540 12 T 1.31 × 12 A +0.0825 2.48 × 1.81.8 15 T 4.4 18 T 3 T +0.034 2.37 × 4.44.4 18 T 21 T +0.027 (2.93 × 4.4 3 A4.4 +0.627 3.41 × 6 A +0.0430 5.76 × DML ) orientation1.8 (cm) 3 T (N) +0.408 2.67 × (N) forces1.8 (N) 12 T +0.312 (N) (1.58 × (N) (N)attack thrustof (N) 4.4 15 T4.4 +0.325 (2.32 × 24 T +0.866 (2.98 × (cm and altitude Lift jet thrust balance directed Drag force jet thrust reaction horizontal sequence with angle Swimming mechanics and behaviour of Lolliguncula brevis 3673 90.2 91.3 67.3 65.5 61.3 58.4 52.2 51.9 33.1 45.6 36.3 3 3 4 3 3 3 3 3 4 4 4 − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 8.90 × 3.50 × 3.53 × 1.56 × 1.14 × 7.31 × 3.94 × + 2.20 × − − + 2.22 × − − − − − 51.5 51.355.1 +3.56 × 31.4 41.134.2 +2.20 × 43.2 22.8 )) 3.6 ) 4.0 1.7 4 4 4 4 3 3 3 3 4 4 4 − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 ction, negative values represent forces acting in the values ction, negative without contribution reaction % of drag 1.90 × 5.10 × 3.00 × 4.91 × 6.73 × 7.17 × 8.17 × 1.01 × 1.25 × 1.62 × 1.14 × Horizontal − − − − − − − − ( − ( − ( − force balance Potential % Acceleration ere was some minor net change in elevation over video over some minor net change in elevation ere was 4 4 4 3 3 3 3 3 3 2 2 − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 4.61 × 6.38 × 5.85 × 1.78 × 1.44 × 2.42 × 2.14 × 3.86 × 5.10 × 1.22 × 1.68 × 4 4 4 4 4 4 4 3 3 3 3 − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 Refilling Horizontal acceleration of fins to video over associated 1.22 × 5.90 × 8.10 × 1.78 × 2.81 × 3.00 × 6.27 × 7.22 × 9.06 × 9.51 × 1.07 × − − − − − − − − − − − ) ) ) 4 3 3 3 3 3 3 3 3 3 3 − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 Continued 7.72 × 1.03 × 1.00 × 1.97 × 1.73 × 2.74 × 2.81 × 3.93 × 4.07 × 6.81 × 9.00 × − − − − − − − − − − − Table 4. Table 7.2 71.9 58.3 51.8 44.0 47.5 24.1 22.4 Potential % contribution contribution )0( )0( )0( ) (76.4) ) (66.5) ) (61.7) ) (56.2) ) (55.2) ) (43.0) ) (43.1) ) (14.0) 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Vertical Vertical of fins to 8.38 × 7.30 × 6.77 × 6.16 × 6.05 × 4.72 × 4.73 × 1.54 × 7.89 × 6.40 × 5.69 × 4.83 × 5.22 × 2.64 × 2.45 × 7.89 × − − − − − − − − − − − − − − − − (+9.70 × (+3.83 × (+6.06 × 3 3 3 3 3 3 3 3 3 3 3 − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 Vertical Vertical force upward- 2.20 × 2.43 × 2.65 × 2.77 × 2.61 × 3.13 × 3.45 × 2.66 × )( )( )( )( )( )( )( )( ) 4.32 × ) 5.12 × ) 6.03 × 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 − − − − − − − − − − − − − − − − − − − 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 (3.87 × (1.24 × (1.55 × (2.04 × (2.31 × (3.12 × (2.79 × (6.77 × 0.0780 3.37 × 0.0645 5.07 × 0.0893 8.76 × − − − ) of 1 − Swimming In the vertical direction, lift, vertical jet thrust and vertical fin thrust must equal buoyant weight at constant elevation. Th weight at constant elevation. fin thrust must equal buoyant jet thrust and vertical direction, lift, vertical In the vertical ceased. fin activity columns indicate where observed Lines in the potential % fin contribution weight); in the horizontal dire the flume floor (i.e. buoyant represent forces towards values direction, negative In the vertical in parentheses are based on force measurements from models without fins. Values DML, dorsal mantle length; A, arms-first; T, tail-first. DML, dorsal mantle length; A, arms-first; T, Squid velocity Change size (cm s 7.6 6 A +0.196A 7.6 2.63 × 7.6 6 6 TA+0.03227.6 +0.107 2.14 × 7.6 9 3.14 × 9 T A 7.67.6 12 12 T +0.01747.6 5.20 × 15 T +0.787 7.52 × 7.6 24 T+0.1737.67.6 24 (1.10 × 21 T +0.328sequences, which is depicted in the change of altitude column. In horizontal direction, drag and refilling force should equal horizontal jet thrust and fin thrust, the (9.68 × and horizontal force imbalances were vertical negative and horizontal fin thrust were not measured directly, Since vertical a jet cycle. acceleration reaction should equal zero over considered as potential fin thrust. (e.g. drag). direction of free-stream flow DML ) orientation7.6 (cm) 3 T (N) (N) forces (N) (N)7.6 (N) 18 T +0.572 (N) (7.62 × attack thrustof (N) (cm and altitude Lift jet thrust balance directed Drag force jet thrust reaction horizontal sequence with angle 3674 I. K. Bartol, M. R. Patterson and R. Mann

0.01 Vertical forces 7

0.0075 ( c m ) 6.5 6 H ei gh t 0.005 5.5 0 0.5 11.5 2 Time (s) 0.0025 Buoyant weight Lift 0 Vertical jet thrust Balance of forces -0.0025

-0.005

(N) 00.25 0.5 0.75 11.25 1.5 1.75 2

orce 0.01 F Horizontal forces

0.005

Drag 0 Acceleration reaction Horizontal jet thrust -0.005 Refilling force Balance of forces

-0.01

-0.015 00.25 0.5 0.75 11.25 1.5 1.75 2 Time (s)

Fig. 10. Vertical and horizontal forces acting on a 4.4 cm Lolliguncula brevis swimming tail-first at 15 cm s−1. In the vertical forces graph, negative values represent forces acting towards the flume floor (i.e. buoyant weight), whereas in the horizontal forces graph negative values represent forces acting in the direction of the free-stream flow (e.g. drag). Since there was some net altitude change over the 2 s video sequence, the height of L. brevis above the flume floor is displayed next to the vertical forces graph. There was no net horizontal change over the video sequence. Fin thrust contributions are not included in the figure. mantle and arms were positioned at high angles of attack that In addition to increasing the angle of attack of the mantle maximized lift but that also had relatively low lift-to-drag and arms, lift was generated by directing high-velocity jets of ratios. Thus, low-speed lift generation took precedence over water downwards and by relying on fin activity. At 3–6 cm s−1, low-speed drag reduction. In fact, up to 91 % of the drag at the funnel was positioned at very high angles of attack speeds of 3–6 cm s−1 was associated with elevating the angle (frequently greater than 50 °) while swimming both tail- and of attack of the mantle and arms. This finding is consistent with arms-first and, consequently, more jet thrust was directed the hydrodynamic study of O’Dor (O’Dor, 1988) on Loligo vertically than horizontally. As pointed out by Vogel (Vogel, opalescens, in which the maintenance of vertical position 1994) and evident from high low-speed energetic costs (Bartol required 66–92 % of the total force at 10 cm s−1, which was the et al., 2001b), directing a jet downwards is an inefficient lowest speed examined. method of hovering and maintaining vertical position. The fins Swimming mechanics and behaviour of Lolliguncula brevis 3675 were very active at low speeds, and vertical force imbalances 1996). Brief squid fins flapped in a dorsoventral axis while a indicated that the fins are responsible for as much as 83.8 % of travelling wave moved in an anteroposterior direction. The the vertical thrust at such speeds. presence of both a fin wave and fin flapping are typical of Positioning the body and appendages at high angles and loliginids but not of ommastrephids, which use only actively moving the fins are critical for lift generation at low dorsoventral flapping, or cuttlefish, which employ only an speeds; however, these behaviors may also be critical for anteroposterior fin wave (Hoar et al., 1994). Furthermore, the stability control. The effectiveness of control surfaces on pronounced sideways S-shaped fin wave observed at low human-designed underwater vehicles, such as submarines and speeds is more characteristic of drag-based propulsion, while autonomous underwater vehicles [see Patterson and Sias the inverted V-shaped wave with distal portions positioned at (Patterson and Sias, 1998)], diminishes at low speeds when the obtuse angles relative to the oncoming flow observed at forces generated by these surfaces become small compared with intermediate/high speeds resembles lift-based propulsion overall inertial forces. This also applies to fishes and squid. (Lauder and Jayne, 1996). Positioning the body and appendages at high angles of attack Drag-based propulsion is most effective at low speeds when increases drag, requiring the propulsors (i.e. fins) to beat more the fin or fin wave moves backwards faster than the animal’s rapidly to provide more thrust. This increased thrust is better forward progression (Westneat, 1996), while lift-based matched to body inertia, a force that can provide significant propulsion is most effective at higher speeds and when the resistance to the return of aquatic organisms to desired paths at local Reynolds number (Re) of the fin is >1000 (Blake, 1983a; low speeds, and thus provides greater stability control (Webb, Webb and Weihs, 1986; Seibel et al., 1998). At low speeds, fin 1993; Webb, 2000). In addition to brief squid, increased wave progression was greater than swimming speed, but at body/arm angles of attack coupled with active fins at low speeds intermediate and high speeds, wave progression was less than for purposes of stability control have been observed in neutrally swimming speed (even with an increase in fin speed with buoyant fishes, such as trout and bluegill (Webb, 1993). swimming velocity). Values of local Re computed for the fins, using chord length as the length variable, are close to the Fin contribution to locomotion Re=1000 transition; Re approaches 1000 at 12, 9, 6 and O’Dor (O’Dor, 1988) estimated that the fins of Loligo 3cms−1 for 1.0–2.9, 3.0–4.9, 5.0–6.9 and 7.0–8.9 cm DML opalescens and Illex illecebrosus contribute 38 and 25 %, squid, respectively. On the basis of the shape changes of the respectively, to overall horizontal thrust at the lowest speed trailing fin wave with speed, variation in travelling wave speed considered in swimming analyses (10 cm s−1), but that the fins relative to swimming speed and local fin Re near 1000, it is play no role in thrust production at higher speeds likely that squid fin movement involves both drag- and lift- (20–140 cm s−1) since, at these speeds, fin trailing wave speeds based propulsive mechanisms, as has also been observed for are lower than swimming velocity. Moreover, Webber and pectoral fin activity in largemouth bass (Lauder and Jayne, O’Dor (Webber and O’Dor, 1986), O’Dor (O’Dor, 1988) and 1996). Since drag and lift are both products of the same O’Dor and Webber (O’Dor and Webber, 1991) assumed that circulatory mechanisms, obscuring the line between drag- and the fins of Loligo opalescens and Illex illecebrosus play only lift-based mechanisms is not uncommon, especially when minor roles in lift generation and are used primarily for control angles of attack are high in unsteady flows (Dickinson, 1996). and steering. For Lolliguncula brevis, which swims at lower One caveat in suggesting that lift-based mechanisms occur sustained swimming speeds than Loligo opalescens or Illex in Lolliguncula brevis fin movement is that, at higher speeds illecebrosus, the fins appear to be important for both vertical when lift-based propulsive mechanisms were presumably and horizontal thrust production over a broad range of operating, fin activity and amplitude decreased and eventually sustained swimming speeds, which is significant since fin ceased in the tail-first swimming mode. Reduction and activity is more economical than jetting (Hoar et al., 1994; termination of fin activity at higher speeds is surprising given Vogel, 1994). In the present study, the fins were used over (i) that lift-based propulsion may still provide thrust at high 50–95 % of the sustained speed range and could account for speeds, even when fin wave speeds are lower than swimming potentially as much as 83.8 % of the total vertically directed speed and (ii) that the fins are more efficient than the jet since force and 55.1 % of the horizontal thrust. they provide continuous thrust and lift throughout the fin cycle Fin activity in Lolliguncula brevis cannot be characterized and interact with larger volumes of water (Hoar et al., 1994; as strictly drag- or lift-based propulsion. In conventional drag- Vogel, 1994). O’Dor and Webber (O’Dor and Webber, 1991), based propulsion, the fins move along an approximate who assumed that only drag-based fin propulsion is operating anteroposterior axis in a ‘rowing’ motion, with the fins in squid, suggested that fin motion ceases when the undulatory perpendicular to the direction of motion during the power waves cannot move backwards faster than the animal moves stroke and parallel to the direction of motion during the forwards because of limitations in shortening speeds of the recovery stroke. In lift-based fin propulsion, the fins move obliquely striated muscle in the fin muscular hydrostat. If this approximately parallel to a dorsoventral axis, and the angle of is true, why is fin flapping/undulation used at all at speeds attack of the fins is adjusted during the fin-beat cycle so that when swimming speed exceeds travelling wave speeds? O’Dor positive thrust is achieved during both the upstroke and the (O’Dor, 1988) found that the fin waves of Loligo opalescens downstroke (Vogel, 1994; Lauder and Jayne, 1996; Westneat, frequently travel at speeds below swimming velocities, but 3676 I. K. Bartol, M. R. Patterson and R. Mann suggested that thrust is still possible since fin activity occurs Although rocket motor propulsive efficiency and whole- during refilling when the squid slows down. Although fin cycle propulsive efficiency arguably characterize the jet activity was sometimes observed in L. brevis during refilling locomotive system in squid more effectively than Froude at high speeds (when fin wave speed was lower than swimming efficiency, none of the above efficiencies completely measure speed), fin activity was more frequently observed during locomotor efficiency in squid. Squid rely on both the jet and mantle contractions. As mentioned above, fin activity is their fins for locomotion and, when both are active (e.g. at probably a composite of drag- and lift-based propulsion, and low/intermediate speeds), the efficiencies above, which conventional rules for either mechanism probably do not apply. account only for jet thrust, do not accurately reflect locomotive The termination and reduction of fin activity may very well be efficiency. Active fins lower the thrust requirements of the jet related to the morphology and physiology of the fin muscular and elevate efficiencies. For example, efficiencies determined hydrostat (Kier, 1988; Kier, 1989) but, because both drag- and during arms-first swimming, when the fins were most active lift-based mechanisms probably underlie fin activity and squid and when the jet was generating the least amount of horizontal are capable of making behavioral adjustments throughout the thrust, were consistently higher than during tail-first jet cycle, fin activity does not simply cease when swimming swimming. Furthermore, the highest efficiencies were detected speeds exceed fin wave speeds. at 9cms−1, when the fins were active and less downward thrust was necessary to counteract negative buoyancy compared with Locomotive efficiency lower speeds. Therefore, when the fins are active, the above Froude efficiencies (ηF) presented in this study for efficiencies should be viewed with caution, but when the fins Lolliguncula brevis swimming tail-first (ηF=28.3–57.5 %) are are inactive, they are useful indicators of efficiency. generally higher than those reported previously for Illex illecebrosus (ηF=12–34 %) swimming over a range of speeds Swimming strategies (O’Dor, 1988). The average Froude efficiency reported by The greater preference for arms-first swimming at low Anderson and DeMont (Anderson and DeMont, 2000) for speeds in swim tunnels followed by a transition to exclusive Loligo pealei swimming at 25 cm s−1 (approximately tail-first swimming at intermediate and high speeds indicates 1 mantle length s−1) was 56 %, which is close to Froude that there are velocity-specific advantages associated with efficiencies of 42.4–57.5 % for L. brevis swimming at 6–9 cm s−1 each swimming mode. Tail-first swimming is probably more (1.1–1.6 mantle lengths s−1). Interestingly, Anderson and preferable at high speeds because the funnel does not need to DeMont (Anderson and DeMont, 2000) suggest that Froude bend to generate the necessary horizontal thrust. In arms-first efficiency, which is the traditional measure of propulsive swimming, the funnel must curve by approximately 180 ° to efficiency in jet-propelled organisms, underestimates efficiency direct thrust rearwards in a horizontal path, and lateral video during jetting and fails accurately to reflect the intake views of the funnel indicate that some funnel constriction is mechanism of the squid (i.e. in the Froude propulsion approach, concomitant with significant curvature. This constriction in the the momentum of the fluid is continually added to the system funnel significantly lowers expelled water volume flux (J) and not brought to rest, as is the case for squid during refilling). since J is proportional to the fourth power of funnel radius (r) Consequently, they suggest two alternative methods of [J=(πr4/8µ)(∆p/l), where µ is the dynamic viscosity of water computing propulsive efficiency in jet-propelled organisms: (i) and ∆p/l is the pressure gradient (Denny, 1993)]. Therefore, rocket motor propulsive efficiency, which is presumably a better water must be expelled at high velocity to produce thrust estimate of jet efficiency during fluid output than Froude comparable with that generated by a non-constricted funnel. efficiency, and (ii) whole-cycle propulsive efficiency, which Since E=1/2mv2, where E is energy, m is mass and v is velocity, more accurately reflects the balance of energy during fluid and energy requirements scale with the square of expelled output and input than Froude efficiency. Both methods of water velocity, jet-propelled swimming in an arms-first evaluating efficiencies were calculated in the present study. orientation at high speeds is energetically costly. Anderson and DeMont (Anderson and DeMont, 2000) In L. brevis, funnel constriction during arms-first swimming determined that average rocket motor propulsive efficiency for is presumably most deleterious during the early portion of Loligo pealei was 65 %, which is close to the upper limit of mantle contraction when the funnel expands to maximal rocket propulsive efficiencies reported in this study for L. brevis diameter. During the remainder of the contraction cycle, L. swimming tail-first (rocket propulsive efficiencies for L. brevis brevis actively reduces funnel diameter. O’Dor (O’Dor, 1988) were 32.1–69.4 %). These estimates of output efficiency are and Anderson and DeMont (Anderson and DeMont, 2000) greater than Froude estimates and are closer to maximum detected similar dynamic control of the funnel in Loligo propulsive efficiencies reported for fish (81 %) (Webb, 1971). opalescens and Loligo pealei, respectively. Squid may be Whole-cycle estimates computed by Anderson and DeMont reducing funnel diameter at the end of the jet cycle to maximize (Anderson and DeMont, 2000) for L. pealei (34–48 %) were power output from a given volume change. similar to whole-cycle efficiencies calculated in the present During high-speed tail-first swimming, the fins may be used study for L. brevis (29.0–44.4 %). Both are generally lower than for forward attitude control, steering and lift generation, while Froude and rocket motor efficiency estimates and suggest that the trailing arms, especially the third arms with heavy keels the refilling period is costly for squid. that are often spread out to act as high-aspect-ratio airfoils, may Swimming mechanics and behaviour of Lolliguncula brevis 3677 serve to stabilize the body, adjust pitch and make lift in the force balance equations revealed that jet thrust did adjustments (as was observed during mantle refilling). During increase with speed but that the mechanism(s) responsible for arms-first swimming, the arms, which are located at the leading this increase varied among squid and with speed. Jet thrust edge, collapse into a conical arrangement and play less of a elevation was achieved using one or more of the following role in stabilization and lift adjustment. methods: (i) higher mantle contraction frequency, (ii) greater There are benefits to arms-first swimming as well, especially mantle expansion or (iii) lower funnel angles of attack. High at low speeds. Arms-first swimming allows for greater variability in the mechanism(s) selected to achieve greater jet observance of forward surroundings than tail-first swimming, thrust coupled with limited arms-first data (a more restricted since the eyes are located more anteriorly and the arms may be size range was considered for arms-first swimming than for moved if necessary for clearer forward views. Because prey tail-first swimming) made it difficult to detect consistent strikes occur in an arms-first orientation (Hanlon and behavioral mechanisms for jet thrust enhancement. Messenger, 1996; Kier and van Leeuwen, 1997), arms-first Furthermore, even though fin speed, fin-beat frequency and fin- swimming enables swift prey attacks whenever opportunities beat amplitude did not increase with speed, some additional arise, while tail-first swimming requires rotation to arms-first horizontal thrust may be provided by keeping fin-beat swimming prior to attack. Arms-first swimming is also frequency and amplitude high, lowering the angle of attack of beneficial for defensive posturing during sudden encounters the mantle to which the fins are attached and positioning the with predators (Hanlon and Messenger, 1996). While fins at various angles of attack to maximize lift-based swimming arms-first, the fins are located near the trailing edge, propulsion. which reduces interaction between the fin wake and the body, O’Dor (O’Dor, 1988) reported four distinct gaits in L. and this consequently enhances fin propulsion and efficiency opalescens during tail-first swimming that were related to the (Lighthill and Blake, 1990; Daniel et al., 1992). use of collagen springs in the mantle. In the present study, As mentioned above, maximizing fin propulsion and some similar behavioral transitions were detected in L. brevis efficiency is advantageous since, unlike jet propulsion, fin during tail-first swimming, but overall behavioral changes locomotion provides continuous lift and thrust throughout the tended to be more gradual over the sustained speed range fin cycle and affects relatively large volumes of water with considered, with behavioral differences most apparent when each fin stroke. Optimal fin placement, high fin thrust comparing size classes. For example, O’Dor (O’Dor, 1988) efficiency and volume flux limitations associated with funnel found that the amplitude of mantle expansion for L. opalescens bending and jetting all contributed to greater reliance on fin was initially low at low speeds (10 cm s−1), but then increased propulsion and less on jetting during arms-first swimming. In significantly and remained constant over a broad range of fact, neither fin-beat frequency nor fin amplitude decreased speeds between 20 and 40 cm s−1, only to increase again at appreciably with speed during arms-first swimming, as was critical speeds of 50 cm s−1 and at burst speeds of 140 cm s−1. observed in tail-first swimming, despite the fact that swimming For brief squid, mantle expansion generally increased speeds exceeded fin speeds at higher velocities. (This is further consistently with speed during tail-first swimming and did not evidence that drag-based propulsion is not necessarily the only remain constant over a broad range of speeds. One notable mechanism underlying fin motion in L. brevis.) The degree of exception was squid in the 1.0–2.9 cm DML size class, which funnel bending and volume flux limitations during arms-first did not vary the amplitude of mantle expansion significantly swimming were reduced by positioning the funnel at high over the entire range of swimming speeds. angles of attack (on average, funnel angles of attack were 15 ° During tail-first swimming, angles of attack and fin-beat greater during arms-first swimming than during tail-first amplitude decreased linearly with speed for all size classes of swimming) and relying on the jet more for vertical than for brief squid, and mantle contraction frequency either remained horizontal thrust. Because less dynamic lift from flow over the constant (size classes >3 cm DML or more) or increased body was required when the funnel was positioned at high steadily with speed (size class <3 cm DML). O’Dor (O’Dor, angles of attack during arms-first swimming, composite 1988) found that mantle contraction frequency of adult L. mantle/arm angles of attack were reduced (on average, opalescens remains relatively constant with speed, and Webber composite angles were 6 ° lower relative to tail-first swimming) and O’Dor (Webber and O’Dor, 1986) found that contraction and lift-to-drag ratios increased as profile drag and induced frequency of Illex illecebrosus increases from 28 to 48 cm s−1 drag were reduced by the change in angle of attack. Most of but that, above 48 cm s−1, contraction frequency increases less the adjustment in angle of attack was achieved by lowering arm steeply or remains constant with elevated swimming speed. angles of attack and not mantle angles of attack. O’Dor (O’Dor, 1988) reported that the fins beat twice with No consistent increase in mantle contraction frequency, each mantle contraction at 10 cm s−1, once during refilling over mantle expansion, fin activity, fin amplitude, fin speed or fin a broad range of speeds between 20 and 40 cm s−1, and not at downstroke time with increasing speed was observed during all at both sustained and burst speeds above 50 cm s−1. In the arms-first swimming. Where then does the extra thrust come present study, fin activity during tail-first swimming generally from to power locomotion at higher speeds? Unlike tail-first decreased linearly with swimming speed until sub-critical swimming, no one dominant mechanism was responsible for speeds, at which the fins simply wrapped around the mantle. thrust elevation. An examination of the three squid considered The exception again was squid within the 1.0–2.9 cm DML size 3678 I. K. Bartol, M. R. Patterson and R. Mann class, which abruptly shifted from 2 fin beats s−1 at 9cms−1 to resonant elastic spring system. There are ontogenetic none at 12 cm s−1. As mentioned above, fin flapping did differences in the arrangement, mechanical properties and sometimes coincide with refilling at intermediate speeds when physiological properties of the mantle musculature of squid, fin activity was low, but fin flapping was more frequently especially mantle connective tissue (Thompson, 1997; coupled with mantle contraction at intermediate speeds. Thompson, 1998), but these differences contribute to reduced Moreover, at low speeds when fin activity was high, fin mantle expansion and increased muscle shortening with age flapping was often coupled with both refilling and contraction. (size). Therefore, these differences do not help explain the Finally, mantle refilling times were greater than mantle observed dichotomy in swimming strategies. contraction times, as was suggested by O’Dor (O’Dor, 1988), but for most of the size classes, refilling did not occur Unsteady mechanisms progressively faster over a range of speeds. The exception was The differences in contraction rates and swimming strategies squid in the small size class (1.0–2.9 cm DML), which refilled may relate to hydrodynamics and vortex ring formation, which and contracted their mantles progressively faster with was observed in L. brevis. Our current understanding of vortex swimming speed during tail-first swimming. ring phenomena is reviewed nicely by Shariff and Leonard To swim at higher speeds, small squid (DML<3.0 cm) (Shariff and Leonard, 1992) and Lim and Nickels (Lim and swimming tail-first increased contraction frequency and kept Nickels, 1995). In the context of jet propulsion, vortex rings mantle expansion relatively constant, whereas squid belonging are beneficial because they entrain additional water from to the larger size classes (DML 3.0 cm or more) increased surrounding areas and increase the amount of fluid driven mantle expansion and kept contraction rates relatively backwards in the jet wake. Since jet thrust is the product of the constant. The dichotomy in swimming approaches was mass (per unit time) and the velocity of water expelled probably not a result of differences in relative speed ranges. backwards, additional ambient water accelerated by the Although a broader range of relative swimming speeds vortex rings may elevate thrust. This was demonstrated was considered for squid less than 3 cm in DML experimentally by Krueger (Krueger, 2001), who found that (1.25–6.37 DML s−1) than for squid more than 5 cm in DML the impulse associated with vortex ring formation is (0.41–3.33 DML s−1), squid 3.0–4.9 cm in DML were examined significantly larger than that expected from the jet velocity over a similar speed range (0.82–6.21 DML s−1) to that of alone. Interestingly, Gharib et al. (Gharib et al., 1998) smaller squid, yet did not increase mantle contraction demonstrated that there is a limit to the amount of energy or frequency with speed. Furthermore, even within the speed circulation that enters a developing vortex ring during jetting. range 0–3 DML s−1, mantle contraction frequency for squid less This limit occurs when the ratio of the length (l) of a plug of than 3 cm in DML increased with speed, and mantle expansion fluid forced through a tube to the diameter d of the tube is was relatively constant. 3.6–4.5, which is known as the formation number. When the The observed behavioral differences in swimming l/d ratio (stroke ratio) is greater than approximately 4, the approaches among size classes do not appear to be related to vortex ring no longer grows in strength but rather ‘pinches off’ the mantle musculature. Squid mantle tissue functions as a from the jet, and the remaining fluid in the pulse is simply constant-volume system with a three-dimensional array of ejected as a trailing jet. This pinch off phenomenon also has tightly bundled muscles commonly called a muscular significance for propulsion since it was shown that the hydrostat (Kier and Smith, 1985; Smith and Kier, 1989). formation of a vortex ring generates proportionally more When circular muscles shorten during mantle contraction, impulse per unit of ejected fluid than does a trailing jet they increase in diameter, causing the mantle wall to thicken. (Krueger, 2001). Obliquely oriented collagen fibers traversing the thickness of Given that funnel diameter (d) and expelled water volume (v) the mantle wall are strained and store energy at times in the were known in our experiment, l/d ratios could be calculated jet cycle when, because of the geometry of the locomotor for L. brevis from v=π/4(d2)l. Large and intermediate-sized apparatus, the circular muscles cannot do useful squid generally had l/d ratios far in excess of 4, ranging from hydrodynamic work (Gosline and Shadwick, 1983; Pabst, 10 to 40. However, smaller squid (DML<3.0 cm), which have 1996). Elastic energy stored in the collagen fibers powers larger relative funnel diameters, had lower l/d ratios overall, much of the refilling phase of the jet cycle, although ranging from 3 to 17; some smaller squid even kept formation contraction of radially oriented muscle fibers, which extend numbers between 4 and 7 throughout various jet cycles. from the inner to outer surface of the mantle, also plays a role Consequently, by keeping expelled water volume low and in refilling (Gosline and Shadwick, 1983; Gosline et al., 1983; increasing mantle contraction rates with speed, smaller squid Kier, 1988). The elastic spring system within the mantle is may be maximizing impulse per unit time and possibly for a non-resonant, depending simply on the degree of loading by given energy input. Simply keeping the spacing between vortex the circular muscles, and the system does not have to be driven rings low by increasing contraction rates with speed may also at or near its natural frequency, as is the case with improve thrust. Weihs (Weihs, 1977) suggests that propulsive hydromedusan jellyfish (DeMont and Gosline, 1988; Pabst, benefits increase as pulse rate increases and separation between 1996). Therefore, the constant rates of mantle contraction vortex rings decreases because vortices are able to interact, observed in larger squid are probably not the products of a producing a greater overall translational velocity. Smaller squid Swimming mechanics and behaviour of Lolliguncula brevis 3679 that have relatively larger funnel orifices and that expel angles of attack (when the models were closer to the wall) may relatively small volumes of water at high frequency may benefit have elevated force measurements, as observed by Sarpkaya from this vortex ring interaction. Conversely, larger squid that (Sarpkaya, 1976) for cylinders near solid surfaces. If expel larger volumes of water at high speeds through relatively interactive effects confounded high-angle force measurements, small funnel diameters probably produce vortex rings that are then acceleration reaction measurements at low speeds may be too widely spaced to benefit significantly from ring interaction. high; however, at higher speeds when angles of attack were Thus, increasing mantle contraction rate (to keep ring spacing lower, added mass coefficients were within the range of those low) with speed presumably does not augment thrust of other biological organisms, and the acceleration reaction significantly for intermediate/large squid, allowing for the was still the dominant instantaneous force. The net acceleration selection of more cost-effective mechanisms for increasing reaction did not approach zero over several jet cycles as thrust with speed, such as increasing expelled water volume. predicted by Daniel (Daniel, 1983; Daniel, 1984), especially as Interestingly, other studies have suggested that thrust benefits the speed and the range of accelerations and decelerations may actually be reduced at high pulse rates because vortex rings increased. However, this is not surprising given that begin to interfere negatively with each other (Krueger, 2001). measurement errors are often magnified when taking the Clearly, quantitative measurement of the wake structure of second derivative of positional changes (even those that have squid of different sizes, using techniques such as two- been smoothed) to compute acceleration. dimensional digital particle image velocimetry and three- Unsteady aspects of flow probably affect other components dimensional defocusing digital particle image velocimetry of thrust and lift production in L. brevis. As discussed above, (Pereira et al., 2000), is necessary to test the above hypotheses jets pulsed at certain frequencies may have advantages over and measure jet wake structure. continuous, steady jets. Anderson and DeMont (Anderson and Since squid rely on a pulsating jet for propulsion, they swim DeMont, 2000) demonstrate that peak thrust predictions using in an unsteady fashion, constantly accelerating and decelerating an unsteady approach are better matched to axial velocities as they move through the water and experience a force known than quasi-steady approaches, and unsteady analyses predict as the acceleration reaction, which resists changes in the negative jet pressures in the mantle near the end of the jet period animal’s velocity (Batchelor, 1967; Webb, 1979; Daniel, 1983; that are not predicted using quasi-steady methods. Using Daniel, 1984; Daniel, 1985; Vogel, 1994). In his work with three-dimensional kinematic data, bio- and hydromechanical jetting medusae, Daniel (Daniel, 1983; Daniel, 1984) found that modeling and/or electromyography, Daniel (Daniel, 1988), the acceleration reaction is an important instantaneous force, Lauder and Jayne (Lauder and Jayne, 1996) and Westneat often far outweighing drag at a given point in the jet cycle, but (Westneat, 1996) offer evidence that the acceleration reaction that the relative contribution of the acceleration reaction provides propulsive thrust during fin motion in fishes both averaged over a jet cycle is much smaller. Moreover, when during dorsoventral flapping and during anteroposterior rowing. starting from rest, the relative importance of the acceleration Dickinson and Götz (Dickinson and Götz, 1996), using reaction in resisting movement averaged over a jet cycle is sensitive force measurement and flow visualization equipment, approximately 50 %, but after several jet cycles the acceleration demonstrated that unsteady movements in insect wings reaction contributes less than 5 % of resistance. This is because dramatically elevate lift and thrust. Given that flow around the acceleration reaction resists both acceleration and squid fins is unsteady as a result of pulsatile swimming and fin deceleration and, consequently, changes direction during the velocity changes during upstrokes and downstrokes, unsteady cycle. During steady swimming, mean acceleration and flow components assuredly affect vertical and horizontal fin deceleration should balance out over a cycle or the organism thrust, although the effects were not examined directly in the would increase or decrease velocity, respectively. Therefore, the present study. Unsteady movements of the arms, appendages net acceleration reaction over the cycle should approach zero. that have been largely ignored in other squid swimming studies, As was the case with Daniel’s (Daniel, 1983; Daniel, 1984) also are intriguing. The arms of L. brevis are sometimes work with swimming medusae, the acceleration reaction of L. positioned at very high angles of attack, which produces flow brevis was the most important instantaneous force during the separation and the likely development of attached bubble jet cycle, and the relative contributions of the acceleration vortices that may produce added lift for the head. Unsteady reaction averaged over a cycle were much smaller than the jetting movements coupled with rapid arm oscillation from high instantaneous contributions. The instantaneous contribution of to low angles of attack (behaviors that were often observed in the acceleration reaction was even greater relative to L. brevis) may help generate, stabilize and retain these attached instantaneous drag (and lift) for L. brevis, which positions its vortices, as oscillating wings in insects do to provide thrust and mantle, arms and fins at various angles of attack, than reported lift enhancement (Dickinson and Götz, 1996). by Daniel (Daniel, 1983; Daniel, 1984) for medusae, which swam in a horizontal orientation. The added mass coefficients Concluding remarks reported in the present study for squid at high angles of attack The data presented above provide an overview of the are larger than those reported for other biological organisms swimming behavior and mechanics of a slow-swimming squid, (Denny, 1988; Daniel, 1983). Thus, there is some concern that Lolliguncula brevis, over a range of sizes and speeds and at interactions between the model and the flume walls at high various swimming orientations. On the basis of the results of 3680 I. K. Bartol, M. R. Patterson and R. Mann this study, L. brevis clearly uses complex interactions between Chamberlain, J. A., Jr (1981). Hydromechanical design of fossil the mantle, fins, arms and funnel during locomotion. Given that cephalopods. Syst. Ass. Spec. 18, 289–336. Chamberlain, J. A., Jr (1990). 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